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STA301 GDB No 1 Solution Autumn 2021-VU GDB Solutions-VU


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STA301 GDB No 1 Solution 2021, Vu gdb solutions, #variance, #standard_deviations, virtusl university, STA630 GDB No 1 Solution Autumn 2021, #pie_chart, #bar_chart,
Transcript
00:00In the name of Allah, the most Gracious, the most Merciful.
00:02Peace be upon you, dear students and viewers.
00:04Welcome to my YouTube channel, DJ Learner Point.
00:06In today's video tutorial,
00:08we will solve the DDB number 1
00:10of Statistics and Probability
00:12whose subject code is STA309.
00:14Its total marks are 8
00:16and its closing date is
00:1812th December 2021
00:20and the date will be Sunday.
00:22So, let's read the
00:24question descriptions.
00:26In this DDB,
00:28we have two questions
00:30and I think each question
00:32have equal marks 4-4.
00:34This is mine, but someone
00:36must have mentioned it.
00:38But I have got it.
00:40Why do we
00:42need to compute the measure of
00:44dispersion, variance
00:46and standard deviation, even if we have
00:48computed the measure of central
00:50tendency, mean, median and mode, etc.
00:52Question number 2.
00:54What is the difference between pie chart and
00:56pie chart? Why do we use them?
00:58There are two parts of this question.
01:00So, let's go to our answer.
01:04The answer of question number 1 is
01:06As measuring mean,
01:08median and mode, etc. tell us
01:10about the location of data
01:12as center or tendency of data
01:14towards center value.
01:16The tools
01:18of measuring
01:20center tendency
01:22mean, median and mode
01:24tell us about
01:26center location of data
01:28where data values move
01:30and determine
01:32center tendency of data.
01:34Measure of dispersion
01:36depicts variability between fitted values
01:38and data values or actual observations.
01:40Measure of
01:42dispersion
01:44determines
01:46the variability
01:48of variance and standard deviation.
01:50Now,
01:52if you have only one data,
01:54then you plot it,
01:56then you draw fitted values,
01:58then you draw fitted values,
02:00then you draw fitted values,
02:02then you draw fitted values,
02:04then you draw fitted values,
02:06then you draw fitted values,
02:08then you draw fitted values,
02:10then you draw fitted values,
02:12then you draw fitted values,
02:14then you draw fitted values,
02:16then you draw fitted values,
02:18then you draw fitted values,
02:20Further, standard deviation is
02:22the square root of variance and recall that
02:24variance is the second moment about mean.
02:26You know that
02:28I will share a very important point
02:30with you.
02:34The first moment about mean
02:36i.e. sum of deviation from mean
02:38is always equal to zero.
02:40That's why we take its square.
02:42i.e. x-bar whole square
02:44or x-bar for sample data
02:46whole square.
02:48We take its square root
02:50in the end
02:52so that we can measure its actual values.
02:54So, this is the philosophy
02:56behind the variance
02:58and standard deviation
03:00square and square root.
03:02Now, there are two parts of it.
03:04We have to tell the difference
03:06in pie chart and bar chart
03:08and when we use it.
03:10In pie chart, we have different
03:12pie segments or sectors
03:14which are made up of a circle form.
03:16In pie chart, we have
03:20pie segments or sectors
03:22which are made up of a circle form.
03:24In pie chart, we have
03:26pie segments or sectors
03:28which are made up of a circle form.
03:30This is what we call as a circle.
03:34Area of every pie is
03:36sliced as ratio to its
03:38proportion and total quantity.
03:40Area of every pie
03:42is sliced as ratio to its
03:44is proportional to the total quantity and we show it in percentage in relation with
04:00angle of 30-60 degree, that is, we know that the angle of the circle is 30-60 degree, so
04:12first of all, we have to find out the degree of every sector or slice that we have, after
04:21that, when we know its degree, then we determine its percentage, that is, the component divided
04:30by the total quantity, the total output we have into 360, so the angle will come and the
04:38first portion will come to us in percentage form, to identify the contribution of every
04:43slice, we use different colors for every slice or pipe, so we can use the same thing in bar
04:50charts also, now bar charts consist of rectangle shaped bars, every bar is shaded and has equal
05:01width and length, and the length and width of each bar will be equal, width will be equal
05:17width and length will not be equal, okay, I will elaborate it a little, width has equal
05:31width and length, we are talking about individual bar, so definitely the length of the second
05:40bar will be different, but its width on x-axis will be same, as it is, we do not give much
05:51importance to it in bar chart, length is important for us, so it varies as per to the corresponding
05:58values of the data, so in time series data, we use vertical bars, now the bar charts have
06:06different categories, when do we use vertical bars, we use vertical bars to represent the
06:15values to the corresponding period in absolute term, we used vertical bars to represent the
06:26values to the corresponding period in absolute term, we used vertical bars to represent the
06:33values to the corresponding period in absolute term, we used vertical bars to represent the
06:40values to the corresponding period in absolute term, we used vertical bars to represent the
06:47values to the corresponding period in absolute term, we used vertical bars to represent the
06:52values to the corresponding period in absolute term, we used vertical bars to represent the
06:57values to the corresponding period in absolute term, we used vertical bars to represent the
07:03values to the corresponding period in absolute term, we used vertical bars to represent the
07:06values to the corresponding period in absolute term, we used vertical bars to represent the
07:09values to the corresponding period in absolute term, we used vertical bars to represent the
07:11values to the corresponding period in absolute term, we used vertical bars to represent the
07:13values to the corresponding period in absolute term, we used vertical bars to represent the
07:14values to the corresponding period in absolute term, we used vertical bars to represent the
07:15values to the corresponding period in absolute term, we used vertical bars to represent the
07:16values to the corresponding period in absolute term, we used vertical bars to represent the
07:17values to the corresponding period in absolute term, we used vertical bars to represent the
07:18values to the corresponding period in absolute term, we used vertical bars to represent the
07:19values to the corresponding period in absolute term, we used vertical bars to represent the
07:20values to the corresponding period in absolute term, we used vertical bars to represent the
07:21values to the corresponding period in absolute term, we used vertical bars to represent the
07:22values to the corresponding period in absolute term, we used vertical bars to represent the
07:23values to the corresponding period in absolute term, we used vertical bars to represent the
07:24values to the corresponding period in absolute term, we used vertical bars to represent the
07:25values to the corresponding period in absolute term, we used vertical bars to represent the
07:26values to the corresponding period in absolute term, we used vertical bars to represent the
07:27values to the corresponding period in absolute term, we used vertical bars to represent the
07:28values to the corresponding period in absolute term, we used vertical bars to represent the
07:29values to the corresponding period in absolute term, we used vertical bars to represent the
07:30values to the corresponding period in absolute term, we used vertical bars to represent
07:31the values to the corresponding period in absolute term, we used vertical bars to represent
07:32the values to the corresponding period in absolute term, we used vertical bars to represent
07:33the values to the corresponding period in absolute term, we used vertical bars to represent the
07:34values to the corresponding period in absolute term, we used vertical bars to represent the
07:35values to the corresponding period in absolute term, we used vertical bars to represent the
07:36values to the corresponding period in absolute term, we used vertical bars to represent the
07:37values to the corresponding period in absolute term, we used vertical bars to represent the
07:38values to the corresponding period in absolute term, we used vertical bars to represent the
07:39values to the corresponding period in absolute term, we used vertical bars to represent
07:40the values to the corresponding period in absolute term, we used vertical bars to represent
07:41the values to the corresponding period in absolute term, we used vertical bars to represent
07:42the values to the corresponding period in absolute term, we used vertical bars to represent
07:43the values to the corresponding period in absolute term, we used vertical bars to represent
07:44the values to the corresponding period in absolute term, we used vertical bars to represent
07:45the values to the corresponding period in absolute term, we used vertical bars to represent the
07:46values to the corresponding period in absolute term, we used vertical bars to represent the
07:47values to the corresponding period in absolute term, we used vertical bars to represent the
07:48values to the corresponding period in absolute term, we used vertical bars to represent the
07:49values to the corresponding period in absolute term, we used vertical bars to represent the
07:50values to the corresponding period in absolute term, we used vertical bars to represent the
07:51values to the corresponding period in absolute term, we used vertical bars to represent the
07:52values to the corresponding period in absolute term, we used vertical bars to represent the
07:53values to the corresponding period in absolute term, we used vertical bars to represent the
07:54values to the corresponding period in absolute term, we used vertical bars to represent
07:55the values to the corresponding period in absolute term, we used vertical bars to represent
07:56the values to the corresponding period in absolute term, we used vertical bars to represent
07:57the values to the corresponding period in absolute term, we used vertical bars to represent
07:58the values to the corresponding period in absolute term, we used vertical bars to represent
07:59the values to the corresponding period in absolute term, we used vertical bars to represent
08:00the values to the corresponding period in absolute term, we used vertical bars to represent
08:01the values to the corresponding period in absolute term, we used vertical bars to represent
08:02the values to the corresponding period in absolute term, we used vertical bars to represent
08:03the values to the corresponding period in absolute term, we used vertical bars to represent
08:04the values to the corresponding period in absolute term, we used vertical bars to represent
08:05the values to the corresponding period in absolute term, we used vertical bars to represent
08:06the values to the corresponding period in absolute term, we used vertical bars to represent
08:07the values to the corresponding period in absolute term, we used vertical bars to represent
08:08the values to the corresponding period in absolute term, we used vertical bars to represent
08:09the values to the corresponding period in absolute term, we used vertical bars to represent
08:10the values to the corresponding period in absolute term, we used vertical bars to represent
08:11the values to the corresponding period in absolute term, we used vertical bars to represent
08:12the values to the corresponding period in absolute term, we used vertical bars to represent
08:13the values to the corresponding period in absolute term, we used vertical bars to represent
08:14the values to the corresponding period in absolute term, we used vertical bars to represent
08:15the values to the corresponding period in absolute term, we used vertical bars to represent
08:16the values to the corresponding period in absolute term, we used vertical bars to represent
08:17the values to the corresponding period in absolute term, we used vertical bars to represent
08:18the values to the corresponding period in absolute term, we used vertical bars to represent
08:19the values to the corresponding period in absolute term, we used vertical bars to represent
08:20the values to the corresponding period in absolute term, we used vertical bars to represent
08:21the values to the corresponding period in absolute term, we used vertical bars to represent
08:22the values to the corresponding period in absolute term, we used vertical bars to represent
08:23the values to the corresponding period in absolute term, we used vertical bars to represent
08:24the values to the corresponding period in absolute term, we used vertical bars to represent
08:25the values to the corresponding period in absolute term, we used vertical bars to represent
08:26the values to the corresponding period in absolute term, we used vertical bars to represent
08:27the values to the corresponding period in absolute term, we used vertical bars to represent
08:28the values to the corresponding period in absolute term, we used vertical bars to represent
08:29the values to the corresponding period in absolute term, we used vertical bars to represent
08:30the values to the corresponding period in absolute term, we used vertical bars to represent
08:31the values to the corresponding period in absolute term, we used vertical bars to represent
08:32the values to the corresponding period in absolute term, we used vertical bars to represent
08:33the values to the corresponding period in absolute term, we used vertical bars to represent the
08:34values to the corresponding period in absolute term, we used vertical bars to represent the
08:35values to the corresponding period in absolute term, we used vertical bars to represent the
08:36values to the corresponding period in absolute term, we used vertical bars to represent the
08:37values to the corresponding period in absolute term, we used vertical bars to represent the
08:38values to the corresponding period in absolute term, we used vertical bars to represent the
08:39values to the corresponding period in absolute term, we used vertical bars to represent
08:40the values to the corresponding period in absolute term, we used vertical bars to represent
08:41the values to the corresponding period in absolute term, we used vertical bars to represent
08:42the values to the corresponding period in absolute term, we used vertical bars to represent
08:43the values to the corresponding period in absolute term, we used vertical bars to represent
08:44the values to the corresponding period in absolute term, we used vertical bars to represent
08:45the values to the corresponding period in absolute term, we used vertical bars to represent
08:46the values to the corresponding period in absolute term, we used vertical bars to represent
08:47the values to the corresponding period in absolute term, we used vertical bars to represent
08:48the values to the corresponding period in absolute term, we used vertical bars to represent
08:49the values to the corresponding period in absolute term, we used vertical bars to represent
08:50the values to the corresponding period in absolute term, we used vertical bars to represent
08:51the values to the corresponding period in absolute term, we used vertical bars to represent
08:52the values to the corresponding period in absolute term, we used vertical bars to represent
08:53the values to the corresponding period in absolute term, we used vertical bars to represent
08:54the values to the corresponding period in absolute term, we used vertical bars to represent
08:55the values to the corresponding period in absolute term, we used vertical bars to represent
08:56the values to the corresponding period in absolute term, we used vertical bars to represent
08:57the values to the corresponding period in absolute term, we used vertical bars to represent
08:58the values to the corresponding period in absolute term, we used vertical bars to represent
08:59the values to the corresponding period in absolute term, we used vertical bars to represent
09:00the values to the corresponding period in absolute term, we used vertical bars to represent
09:01the values to the corresponding period in absolute term, we used vertical bars to represent
09:02the values to the corresponding period in absolute term, we used vertical bars to represent
09:03the values to the corresponding period in absolute term, we used vertical bars to represent
09:04the values to the corresponding period in absolute term, we used vertical bars to represent
09:05the values to the corresponding period in absolute term, we used vertical bars to represent
09:06the values to the corresponding period in absolute term, we used vertical bars to represent
09:07the values to the corresponding period in absolute term, we used vertical bars to represent
09:08the values to the corresponding period in absolute term, we used vertical bars to represent
09:09the values to the corresponding period in absolute term, we used vertical bars to represent
09:10the values to the corresponding period in absolute term, we used vertical bars to represent
09:11the values to the corresponding period in absolute term, we used vertical bars to represent
09:12the values to the corresponding period in absolute term, we used vertical bars to represent
09:13the values to the corresponding period in absolute term, we used vertical bars to represent
09:14the values to the corresponding period in absolute term, we used vertical bars to represent
09:15the values to the corresponding period in absolute term, we used vertical bars to represent
09:16the values to the corresponding period in absolute term, we used vertical bars to represent
09:17the values to the corresponding period in absolute term, we used vertical bars to represent
09:18the values to the corresponding period in absolute term, we used vertical bars to represent
09:19the values to the corresponding period in absolute term, we used vertical bars to represent
09:20the values to the corresponding period in absolute term, we used vertical bars to represent
09:21the values to the corresponding period in absolute term, we used vertical bars to represent
09:22the values to the corresponding period in absolute term, we used vertical bars to represent
09:23the values to the corresponding period in absolute term, we used vertical bars to represent
09:24the values to the corresponding period in absolute term, we used vertical bars to represent
09:25the values to the corresponding period in absolute term, we used vertical bars to represent
09:26the values to the corresponding period in absolute term, we used vertical bars to represent
09:27the values to the corresponding period in absolute term, we used vertical bars to represent
09:28the values to the corresponding period in absolute term, we used vertical bars to represent
09:29the values to the corresponding period in absolute term, we used vertical bars to represent
09:30the values to the corresponding period in absolute term, we used vertical bars to represent
09:31the values to the corresponding period in absolute term, we used vertical bars to represent
09:32the values to the corresponding period in absolute term, we used vertical bars to represent
09:33the values to the corresponding period in absolute term, we used vertical bars to represent
09:34the values to the corresponding period in absolute term, we used vertical bars to represent
09:35the values to the corresponding period in absolute term, we used vertical bars to represent
09:36the values to the corresponding period in absolute term, we used vertical bars to represent
09:37the values to the corresponding period in absolute term, we used vertical bars to represent
09:38the values to the corresponding period in absolute term, we used vertical bars to represent
09:39the values to the corresponding period in absolute term, we used vertical bars to represent
09:40the values to the corresponding period in absolute term, we used vertical bars to represent
09:41the values to the corresponding period in absolute term, we used vertical bars to represent
09:42the values to the corresponding period in absolute term, we used vertical bars to represent
09:43the values to the corresponding period in absolute term, we used vertical bars to represent
09:44the values to the corresponding period in absolute term, we used vertical bars to represent
09:45the values to the corresponding period in absolute term, we used vertical bars to represent the
09:46values to the corresponding period in absolute term, we used vertical bars to represent the
09:47values to the corresponding period in absolute term, we used vertical bars to represent the
09:48values to the corresponding period in absolute term, we used vertical bars to represent the
09:49values to the corresponding period in absolute term, we used vertical bars to represent the
09:50values to the corresponding period in absolute term, we used vertical bars to represent the
09:51values to the corresponding period in absolute term, we used vertical bars to represent the
09:52values to the corresponding period in absolute term, we used vertical bars to represent the
09:53values to the corresponding period in absolute term, we used vertical bars to represent the
09:54values to the corresponding period in absolute term, we used vertical bars to represent the
09:55values to the corresponding period in absolute term, we used vertical bars to represent
09:56the values to the corresponding period in absolute term, we used vertical bars to represent
10:03the values to the corresponding period in absolute term, we used vertical bars to represent the
10:07values to the corresponding period in absolute term, we used vertical bars to represent the
10:08values to the corresponding period in absolute term, we used vertical bars to represent the
10:09values to the corresponding period in absolute term, we used vertical bars to represent the
10:10values to the corresponding period in absolute term, we used vertical bars to represent the
10:11values to the corresponding period in absolute term, we used vertical bars to represent the
10:12values to the corresponding period in absolute term, we used vertical bars to represent the
10:13values to the corresponding period in absolute term, we used vertical bars to represent the
10:14values to the corresponding period in absolute term, we used vertical bars to represent the
10:15values to the corresponding period in absolute term, we used vertical bars to represent the
10:16values to the corresponding period in absolute term, we used vertical bars to represent the
10:26values to the corresponding period in absolute term, we used vertical bars to represent the
10:27values to the corresponding period in absolute term, we used vertical bars to represent the
10:28values to the corresponding period in absolute term, we used vertical bars to represent the
10:29values to the corresponding period in absolute term, we used vertical bars to represent the
10:30values to the corresponding period in absolute term, we used vertical bars to represent the
10:31values to the corresponding period in absolute term, we used vertical bars to represent the
10:32values to the corresponding period in absolute term, we used vertical bars to represent the
10:33values to the corresponding period in absolute term, we used vertical bars to represent the
10:34values to the corresponding period in absolute term, we used vertical bars to represent the
10:35values to the corresponding period in absolute term, we used vertical bars to represent the
10:36values to the corresponding period in absolute term, we used vertical bars to represent the
10:37values to the corresponding period in absolute term, we used vertical bars to represent the
10:38values to the corresponding period in absolute term, we used vertical bars to represent the
10:39values to the corresponding period in absolute term, we used vertical bars to represent the
10:40values to the corresponding period in absolute term, we used vertical bars to represent the
10:41values to the corresponding period in absolute term, we used vertical bars to represent the
10:42values to the corresponding period in absolute term, we used vertical bars to represent the
10:43values to the corresponding period in absolute term, we used vertical bars to represent the
10:44values to the corresponding period in absolute term, we used vertical bars to represent the
10:45values to the corresponding period in absolute term, we used vertical bars to represent the
10:46values to the corresponding period in absolute term, we used vertical bars to represent the
10:47values to the corresponding period in absolute term, we used vertical bars to represent the
10:48values to the corresponding period in absolute term, we used vertical bars to represent the
10:49values to the corresponding period in absolute term, we used vertical bars to represent the
10:50values to the corresponding period in absolute term, we used vertical bars to represent the
10:51values to the corresponding period in absolute term, we used vertical bars to represent the
10:52values to the corresponding period in absolute term, we used vertical bars to represent the
10:53values to the corresponding period in absolute term, we used vertical bars to represent the
10:54values to the corresponding period in absolute term, we used vertical bars to represent the
10:55values to the corresponding period in absolute term, we used vertical bars to represent the
10:56values to the corresponding period in absolute term, we used vertical bars to represent the
10:57values to the corresponding period in absolute term, we used vertical bars to represent the
10:58values to the corresponding period in absolute term, we used vertical bars to represent the
10:59values to the corresponding period in absolute term, we used vertical bars to represent the
11:00values to the corresponding period in absolute term, we used vertical bars to represent
11:01the values to the corresponding period in absolute term, we used vertical bars to represent
11:02the values to the corresponding period in absolute term, we used vertical bars to represent
11:03the values to the corresponding period in absolute term, we used vertical bars to represent the
11:04values to the corresponding period in absolute term, we used vertical bars to represent the
11:05values to the corresponding period in absolute term, we used vertical bars to represent the
11:06values to the corresponding period in absolute term, we used vertical bars to represent the
11:07values to the corresponding period in absolute term, we used vertical bars to represent the
11:08values to the corresponding period in absolute term, we used vertical bars to represent the
11:09values to the corresponding period in absolute term, we used vertical bars to represent the
11:10values to the corresponding period in absolute term, we used vertical bars to represent the
11:11values to the corresponding period in absolute term, we used vertical bars to represent the
11:12values to the corresponding period in absolute term, we used vertical bars to represent
11:13the values to the corresponding period in absolute term, we used vertical bars to represent
11:14the values to the corresponding period in absolute term, we used vertical bars to represent
11:15the values to the corresponding period in absolute term, we used vertical bars to represent the
11:16values to the corresponding period in absolute term, we used vertical bars to represent the
11:17values to the corresponding period in absolute term, we used vertical bars to represent the
11:18values to the corresponding period in absolute term, we used vertical bars to represent the
11:19values to the corresponding period in absolute term, we used vertical bars to represent the
11:20values to the corresponding period in absolute term, we used vertical bars to represent the
11:21values to the corresponding period in absolute term, we used vertical bars to represent the
11:22values to the corresponding period in absolute term, we used vertical bars to represent the
11:23values to the corresponding period in absolute term, we used vertical bars to represent the
11:24values to the corresponding period in absolute term, we used vertical bars to represent
11:25the values to the corresponding period in absolute term, we used vertical bars to represent
11:26the values to the corresponding period in absolute term, we used vertical bars to represent
11:27the values to the corresponding period in absolute term, we used vertical bars to represent
11:28the values to the corresponding period in absolute term, we used vertical bars to represent
11:29the values to the corresponding period in absolute term, we used vertical bars to represent
11:30the values to the corresponding period in absolute term, we used vertical bars to represent
11:31the values to the corresponding period in absolute term, we used vertical bars to represent
11:32the values to the corresponding period in absolute term, we used vertical bars to represent
11:33the values to the corresponding period in absolute term, we used vertical bars to represent
11:34the values to the corresponding period in absolute term, we used vertical bars to represent
11:35the values to the corresponding period in absolute term, we used vertical bars to represent
11:36the values to the corresponding period in absolute term, we used vertical bars to represent
11:37the values to the corresponding period in absolute term, we used vertical bars to represent
11:38the values to the corresponding period in absolute term, we used vertical bars to represent
11:39the values to the corresponding period in absolute term, we used vertical bars to represent
11:40the values to the corresponding period in absolute term, we used vertical bars to represent
11:41the values to the corresponding period in absolute term, we used vertical bars to represent
11:42the values to the corresponding period in absolute term, we used vertical bars to represent
11:43the values to the corresponding period in absolute term, we used vertical bars to represent
11:44the values to the corresponding period in absolute term, we used vertical bars to represent
11:45the values to the corresponding period in absolute term, we used vertical bars to represent
11:46the values to the corresponding period in absolute term, we used vertical bars to represent
11:47the values to the corresponding period in absolute term, we used vertical bars to represent
11:48the values to the corresponding period in absolute term, we used vertical bars to represent
11:49the values to the corresponding period in absolute term, we used vertical bars to represent
11:50the values to the corresponding period in absolute term, we used vertical bars to represent
11:51the values to the corresponding period in absolute term, we used vertical bars to represent the
11:52values to the corresponding period in absolute term, we used vertical bars to represent the
11:53values to the corresponding period in absolute term, we used vertical bars to represent the
11:54values to the corresponding period in absolute term, we used vertical bars to represent the
11:55values to the corresponding period in absolute term, we used vertical bars to represent the
11:56values to the corresponding period in absolute term, we used vertical bars to represent the
11:57values to the corresponding period in absolute term, we used vertical bars to represent
11:58the values to the corresponding period in absolute term, we used vertical bars to represent
11:59the values to the corresponding period in absolute term, we used vertical bars to represent
12:00the values to the corresponding period in absolute term, we used vertical bars to represent
12:01the values to the corresponding period in absolute term, we used vertical bars to represent
12:02the values to the corresponding period in absolute term, we used vertical bars to represent
12:03the values to the corresponding period in absolute term, we used vertical bars to represent the
12:04values to the corresponding period in absolute term, we used vertical bars to represent the
12:05values to the corresponding period in absolute term, we used vertical bars to represent the
12:06values to the corresponding period in absolute term, we used vertical bars to represent the
12:07values to the corresponding period in absolute term, we used vertical bars to represent the
12:08values to the corresponding period in absolute term, we used vertical bars to represent the
12:09values to the corresponding period in absolute term, we used vertical bars to represent the
12:10values to the corresponding period in absolute term, we used vertical bars to represent the
12:11values to the corresponding period in absolute term, we used vertical bars to represent the
12:12values to the corresponding period in absolute term, we used vertical bars to represent the
12:13values to the corresponding period in absolute term, we used vertical bars to represent the
12:14values to the corresponding period in absolute term, we used vertical bars to represent the
12:15values to the corresponding period in absolute term, we used vertical bars to represent the
12:16values to the corresponding period in absolute term, we used vertical bars to represent the
12:17values to the corresponding period in absolute term, we used vertical bars to represent the
12:18values to the corresponding period in absolute term, we used vertical bars to represent the
12:19values to the corresponding period in absolute term, we used vertical bars to represent the
12:20values to the corresponding period in absolute term, we used vertical bars to represent the
12:21values to the corresponding period in absolute term, we used vertical bars to represent the
12:22values to the corresponding period in absolute term, we used vertical bars to represent the
12:23values to the corresponding period in absolute term, we used vertical bars to represent the
12:24values to the corresponding period in absolute term, we used vertical bars to represent the
12:25values to the corresponding period in absolute term, we used vertical bars to represent the
12:26values to the corresponding period in absolute term, we used vertical bars to represent the
12:27values to the corresponding period in absolute term, we used vertical bars to represent the
12:28values to the corresponding period in absolute term, we used vertical bars to represent the
12:29values to the corresponding period in absolute term, we used vertical bars to represent the
12:30values to the corresponding period in absolute term, we used vertical bars to represent the
12:31values to the corresponding period in absolute term, we used vertical bars to represent the
12:32values to the corresponding period in absolute term, we used vertical bars to represent the
12:33values to the corresponding period in absolute term, we used vertical bars to represent the
12:34values to the corresponding period in absolute term, we used vertical bars to represent the
12:35values to the corresponding period in absolute term, we used vertical bars to represent the
12:36values to the corresponding period in absolute term, we used vertical bars to represent the
12:37values to the corresponding period in absolute term, we used vertical bars to represent the
12:38values to the corresponding period in absolute term, we used vertical bars to represent the
12:39values to the corresponding period in absolute term, we used vertical bars to represent the
12:40values to the corresponding period in absolute term, we used vertical bars to represent the
12:41values to the corresponding period in absolute term, we used vertical bars to represent the
12:42values to the corresponding period in absolute term, we used vertical bars to represent the
12:43values to the corresponding period in absolute term, we used vertical bars to represent the
12:44values to the corresponding period in absolute term, we used vertical bars to represent the
12:45values to the corresponding period in absolute term, we used vertical bars to represent the
12:46values to the corresponding period in absolute term, we used vertical bars to represent the
12:47values to the corresponding period in absolute term, we used vertical bars to represent the
12:48values to the corresponding period in absolute term, we used vertical bars to represent the
12:49values to the corresponding period in absolute term, we used vertical bars to represent
12:50the values to the corresponding period in absolute term, we used vertical bars to represent
12:51the values to the corresponding period in absolute term, we used vertical bars to represent the
12:52values to the corresponding period in absolute term, we used vertical bars to represent the
12:53values to the corresponding period in absolute term, we used vertical bars to represent the
12:54values to the corresponding period in absolute term, we used vertical bars to represent the
12:55values to the corresponding period in absolute term, we used vertical bars to represent the
12:56values to the corresponding period in absolute term, we used vertical bars to represent the
12:57values to the corresponding period in absolute term, we used vertical bars to represent the
12:58values to the corresponding period in absolute term, we used vertical bars to represent the
12:59values to the corresponding period in absolute term, we used vertical bars to represent the
13:00values to the corresponding period in absolute term, we used vertical bars to represent
13:01the values to the corresponding period in absolute term, we used vertical bars to represent
13:02the values to the corresponding period in absolute term, we used vertical bars to represent
13:03the values to the corresponding period in absolute term, we used vertical bars to represent the
13:04values to the corresponding period in absolute term, we used vertical bars to represent the
13:05values to the corresponding period in absolute term, we used vertical bars to represent the
13:06values to the corresponding period in absolute term, we used vertical bars to represent the
13:07values to the corresponding period in absolute term, we used vertical bars to represent the
13:08values to the corresponding period in absolute term, we used vertical bars to represent the
13:09values to the corresponding period in absolute term, we used vertical bars to represent the
13:10values to the corresponding period in absolute term, we used vertical bars to represent the
13:11values to the corresponding period in absolute term, we used vertical bars to represent the
13:12values to the corresponding period in absolute term, we used vertical bars to represent the
13:13values to the corresponding period in absolute term, we used vertical bars to represent
13:14the values to the corresponding period in absolute term, we used vertical bars to represent
13:15the values to the corresponding period in absolute term, we used vertical bars to represent the
13:16values to the corresponding period in absolute term, we used vertical bars to represent the
13:17values to the corresponding period in absolute term, we used vertical bars to represent the
13:18values to the corresponding period in absolute term, we used vertical bars to represent the
13:19values to the corresponding period in absolute term, we used vertical bars to represent the
13:20values to the corresponding period in absolute term, we used vertical bars to represent the
13:21values to the corresponding period in absolute term, we used vertical bars to represent
13:22the values to the corresponding period in absolute term, we used vertical bars to represent
13:23the values to the corresponding period in absolute term, we used vertical bars to represent
13:24the values to the corresponding period in absolute term, we used vertical bars to represent
13:25the values to the corresponding period in absolute term, we used vertical bars to represent
13:26the values to the corresponding period in absolute term, we used vertical bars to represent
13:27the values to the corresponding period in absolute term, we used vertical bars to represent the
13:28values to the corresponding period in absolute term, we used vertical bars to represent the
13:29values to the corresponding period in absolute term, we used vertical bars to represent the
13:30values to the corresponding period in absolute term, we used vertical bars to represent the
13:31values to the corresponding period in absolute term, we used vertical bars to represent the
13:32values to the corresponding period in absolute term, we used vertical bars to represent
13:33the values to the corresponding period in absolute term, we used vertical bars to represent
13:34the values to the corresponding period in absolute term, we used vertical bars to represent
13:35the values to the corresponding period in absolute term, we used vertical bars to represent
13:36the values to the corresponding period in absolute term, we used vertical bars to represent
13:37the values to the corresponding period in absolute term, we used vertical bars to represent
13:38the values to the corresponding period in absolute term, we used vertical bars to represent
13:39the values to the corresponding period in absolute term, we used vertical bars to represent
13:40the values to the corresponding period in absolute term, we used vertical bars to represent
13:41the values to the corresponding period in absolute term, we used vertical bars to represent
13:42the values to the corresponding period in absolute term, we used vertical bars to represent
13:43the values to the corresponding period in absolute term, we used vertical bars to represent
13:44the values to the corresponding period in absolute term, we used vertical bars to represent
13:45the values to the corresponding period in absolute term, we used vertical bars to represent
13:46the values to the corresponding period in absolute term, we used vertical bars to represent
13:47the values to the corresponding period in absolute term, we used vertical bars to represent
13:48the values to the corresponding period in absolute term, we used vertical bars to represent
13:49the values to the corresponding period in absolute term, we used vertical bars to represent

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