PIE CHART | DATA HANDLING|CHAPTER 4| CLASS8| COMPLETE EXPLANATION| INSIGHTFUL MATHS
PIE CHART | DATA HANDLING|CHAPTER 4| CLASS8| COMPLETE EXPLANATION| INSIGHTFUL MATHS
Transcript
00:00Hi everyone, welcome to insightful maths.
00:09In today's session, we are going to discuss a very important topic of data handling class
00:148, which is circle graph or the pie chart.
00:18So we'll discuss how to read a pie chart, all the terms related to pie chart or the
00:23circle graph, and how do we create it, right?
00:26So you are requested to please see the video till end so that you are through with how
00:31to read and how to make a circle graph.
00:34So let's start.
00:37So you can see here, what is a circle graph or a pie chart, the both are same when the
00:42data is represented in the form of a circle.
00:45You can see here, data is represented as certain percentage in the circle.
00:51This representation of the whole is known, which is represented in the form of a circle.
00:59It is a circle graph.
01:00How do we read it?
01:02For example, you can see in this particular circle, different colors are representing
01:07different things.
01:08For example, this color, this is sleeping.
01:11This color is cool.
01:12Then we have playing TV and miscellaneous.
01:15So these are percentages of the activities or the time invested by a child in particular
01:23day.
01:24Okay.
01:25So let us understand what information we can draw out of it.
01:30First of all, a pie graph is used to represent the parts of a whole.
01:35A circle is used to represent the whole.
01:38For example, if I am bifurcating, if I'm showing how 24 hours of a child in particular day,
01:47in which all activities he has used his hours and the percentage, and I need to show it
01:53in the form of a circle graph.
01:55So that is a representation, the total of all these percentages should be 100%.
02:01You should always keep in mind, this is a way to check if your calculation is correct
02:05or not.
02:06When you add all these percentages, the answer should always come as 100%.
02:12Let us analyze what all do we, you know, make out from the given information.
02:19First of all, have a look, sleep 8 hours, school 6 hours, play 3 hours, other miscellaneous
02:27activities 3 hours and homework 4 hours.
02:31So let us first understand these hours, how many total hours this circle is representing.
02:378 plus 6, how much is that?
02:40It is 14, 14 plus 3, 17, 18, 19, 20 plus 4 is 24.
02:50So that means this is representing the amount, this is 24 hours of a day.
02:55And we are trying to show that how the child has invested 24 hours in a day.
03:01So first of all, we need to understand what fraction of a day child has invested in different
03:08activities.
03:09So very first thing you should understand, given information to fraction, how do you
03:14do that?
03:16What is this 24?
03:17This is the total hours.
03:19And how did we get that?
03:20We had just added all the numbers.
03:23This is 24.
03:24What is a fraction?
03:26Fraction is part of a whole, right?
03:29So if I need to know what is the fraction of sleep, okay, let us do one by one.
03:35What is the fraction of sleep?
03:36The child has slept for 8 hours out of 24, right?
03:42Total hours are 24 and the child has slept for 8 hours.
03:46So fraction is 8 by 24.
03:49And what is the simplest form?
03:51It is 8 times 8, 8 times 3 is 24.
03:54That means one third of the time the child has used for sleeping.
04:00Similar manner, let us find what is the fraction of the total hours he has invested in school.
04:07Six hours out of 24.
04:09So this is 6 by 24.
04:11If I go for the simplest form, 6 into 1 is 6, 6 into 4 is 24.
04:17That means total one fourth of the time invested in school.
04:23For play, it is 3 hours out of 24.
04:273 by 24 is what, 3 ones are 3, 3 eights are 24.
04:32It is 1 by 8.
04:34It is again 3, same, 1 by 8.
04:37And this is 4 hours.
04:39So 4 out of 24, 4 ones are 4, 4 six are 24.
04:45So this is how we got the fraction first.
04:47It is very important for you to understand how do we get the fraction.
04:52What we do, given number divided by whatever is the total number, correct, we got the fraction.
05:00Now if the question asks you, what is the percentage of the total which is invested
05:06for let's say sleep, school, play, others, how do we get percentage?
05:11Percent means per 100.
05:14So any fraction can be converted to a percentage if we multiply that by 100.
05:20Very simple, we have already learned in grade 7.
05:24So let us calculate what is the percentage of sleep, okay.
05:30What is the fraction?
05:311 by 3.
05:32Now we are calculating percentage, 1 by 3 into, what is the percentages, 1 by 3 into
05:41100, just multiply that by 100, 100 divided by 3 will come somewhere around 33.33%.
05:50This much is the percentage.
05:52Now next one is one fourth.
05:54Now percentage, how do we calculate?
05:57Fraction multiplied by 100, 100 divided by 4 is what, that is 25.
06:03So 25% for school.
06:06Now for playing, play fraction is 1 by 8, 1 by 8 of 100, right, 4 twos are 8, 4 twos
06:16are 8 and 4 fives are 20, it is 25 by 2.
06:22If I divide 25 by 2, I am going to get 12.5% right.
06:28It was for 1 by 8, here 1 by 8 is again the same.
06:32So percentage here once again will be 12.5%.
06:36Last one is 1 by 6, so 1 by 6 multiplied by 100, 2 threes are 6, 2 fives are 10, 0.
06:45Now have a look here, divide 50 by 3, 3 into 1 is 3, difference 2, 0 now, 3 into 6 is 18,
06:57difference 2 and I can, after decimal I can borrow as many zeros, so 666 will continue.
07:03So you can take the 2 digit, 6.67% We got the percentage of each.
07:11Always mind, percentage to be calculated only when it is asked in the question, otherwise
07:16not required.
07:17This is something very important, what is the central angle, we know that in a circle.
07:24Let's understand from here, we all have seen the protector.
07:28It looks something like this.
07:30What is the complete degree of this protector, total 180 degrees are here.
07:36If I keep one more protector like this, so 180 degree up and what is this angle, this
07:42is again 180.
07:43Is it not making a complete circle, 180 plus 180 is 360 degrees.
07:49So understand, the total angle made within the circle is always 360 degree.
07:59If I have to make this circle graph, within the circle, I need to calculate what is the
08:05angle for each fraction.
08:09It is very important, how do we calculate the angle.
08:13First of all, given information say, we have made fraction, you already know, I have explained
08:19you.
08:20Given information say, fraction made, after this, the fraction should be multiplied with
08:28360.
08:31So what is the step?
08:33First of all, the total information, you have to convert it to fraction.
08:38Now fraction has to be converted to a central angle.
08:44How do we convert?
08:45For example, let us understand using the basic information.
08:49This is a circle, and let's say half of the circle is shaded.
08:54I need to make half, so the fraction I have already got, this is 1 by 2.
08:59What is the total degree, 360.
09:01So 1 by 2 of 360 degrees, how much is that?
09:06It is 180 degrees, and have a look, we have got 180 degree.
09:10If the fraction is 1 4th, how does 1 4th look like?
09:141 4th means, if I divide it in 4 equal part, and I take this fraction, I need to know what
09:20is the degree here.
09:22So 1 by 4 multiplied by 360 degree.
09:26360 by 4 is what?
09:28That is 90 degree.
09:29So you need to measure 90 degree here and then go accordingly.
09:34This will become more clear when we'll do a question.
09:38Have a look at question number 3 here.
09:40This I have picked from exercise 4.1 of data handling.
09:45Draw a pie chart showing the following information.
09:49The table shows the colors preferred by a group of people.
09:54So this is basically the color preference given to you, and we have to show this using
09:59a circle graph.
10:00It is very interesting, and I am pretty sure you are going to like it.
10:04So what did I tell?
10:05Step number 1 is, you have to create a fraction from the given information, right?
10:11Let us make this table, blue, green, red, and yellow, total 4 colors are there.
10:18How many people like blue?
10:2118, green is 9, red is 6, yellow is 3, and the total number of people is 36.
10:28This information is given.
10:30Step number 1, you have to create a fraction.
10:34After fraction, we will create what is the degree or the central angle.
10:39Only this much is required, and we'll be able to make a circle graph.
10:43Now we have to make a fraction.
10:47How many people like blue?
10:4818 out of 36.
10:5118 upon 36 is what?
10:53It is 1 by 2 only.
10:55Okay?
10:56There is no degree yet.
10:57We have just got a fraction.
10:58Let me just erase it.
11:00So the fraction for blue color is 1 by 2.
11:03Now let us see what is the fraction for green.
11:069 people out of 36, 9 x 4 is 36, so have we got the fraction 1 by 4?
11:15The fraction for red color is 6 out of 36, 6 x 1 is 6, 6 x 6 is 36, we got the fraction
11:241 by 6, and the last one is only 3 people like yellow color out of 36.
11:303 x 1 is 3, 3 x 1 is 3, 3 x 2 is 6.
11:34The fraction is 1 by 12.
11:37This much is understood.
11:39Now we need to get a degree from this fraction.
11:45So how do we create degree from the fraction?
11:48Total degrees in a circle are 360.
11:51So now we are finding what is the degree for each color.
11:55Total 360 we say half should be given to blue.
11:59So what is half of 360 degrees?
12:02What is half of 360?
12:04That is 180 degrees.
12:06So we have simply got the degree for blue color.
12:09For green color now, the fraction is 1 by 4.
12:13So 1 by 4 of 360 degree.
12:174 x 9 is 36 along with 0.
12:22Simply we have got 90 degrees.
12:24Now for the red color, the fraction is 1 by 6.
12:291 by 6 of 360 degrees.
12:336 x 6 is 36 along with 0, that is 60 degrees.
12:38And in the last for the yellow color, the fraction is 1 by 12.
12:43And the degree multiplied by 360, 12 x 3 is 36 along with 0, that is equal to 30 degrees.
12:53Just to cross check your calculation, the total of all these degrees should be 360.
12:58Let us check if we have done it correctly or any error is there.
13:01180 plus 90 is how much?
13:06If I add 100 in 180, 280 but it is 10 short, it is 270.
13:11270 and 30, 300 and 60 is 360.
13:16Total is 360, this means till now our calculation is absolutely correct.
13:22Let us learn how to put this in a circle graph.
13:27You have to first make a circle using the compass.
13:31I am drawing freehand, so it may look a little untidy.
13:34But please understand, first you have to make a circle of any, I mean a considerable
13:40radius.
13:41Neither too small nor too big.
13:43An average circle is good to go.
13:45First of all, you will show the biggest degree.
13:50So that major portion of your circle will be covered.
13:53180 degrees is for what?
13:55That is for blue color.
13:57What I will do?
13:58I will try to use the same color.
14:00180 degrees is what?
14:02That is half of the circle.
14:04So what I am going to do, I will just divide the circle into half.
14:09And what is this portion?
14:11I will just color it blue.
14:13This portion is showing the blue color preference.
14:16And degree we already know, it is 180 degrees.
14:19Another color preference is green.
14:23And what is the degree for green?
14:25It is 90 degrees.
14:27Do we know that one fourth of the circle is 90?
14:30So half of this one, something like this.
14:37This one is 90 degrees.
14:39For example, this one, this shaded portion is 90 degrees.
14:44Now what we are going to do, red color preference is 60 degrees.
14:51Now you should know, how you will keep your protector here.
14:57Please understand, for example, this is your protector.
15:00Kept in the downward manner.
15:02For example, I have kept this, understand.
15:08This is a protector.
15:09For example, I have kept it like this.
15:11We have to measure this angle.
15:14So this angle is, if you start measuring from here.
15:18In your protector, zero is here as well and here as well.
15:23I am keeping the center of the protector here.
15:27Just imagine that your protector is here.
15:30It is kept here like this.
15:32You start from the zero here.
15:34Zero, 10, 20, 30.
15:37It will go till 90.
15:39On 30, make a mark and then join it up.
15:43You join it from here.
15:45What was your 30 degree?
15:4730 degree is the last yellow color.
15:51So what, this smaller portion is your yellow color.
15:55This small portion is for yellow color.
15:59Just color it up.
16:00This is 30 and the remaining 60 degree is the red color.
16:06So either you can write red here or you can color it up.
16:10So that is how we have converted the circle graph from the given information.
16:15What are the steps?
16:17Step number one, making the fraction.
16:20Then fraction multiplied by 360 degrees, you will get the degree.
16:24Then you need to learn how to use your protector for measuring the angles here and you can
16:29easily make a circle graph.
16:32Let's do one more question.
16:35The adjoining pie chart, it gives the marks scored in examination by the student.
16:41In English, Hindi, maths, social studies and science, if the total marks obtained by the
16:47students were 540, this is the total.
16:53So total degree is 540.
16:57The given information says the total of the marks is 540.
17:06In which subject did the students score 105 marks?
17:10We don't know, we only know the degree.
17:14Let us understand how to convert this degree to marks.
17:19If the total is 540, how many total degrees are there in the circle?
17:28We have already done this.
17:29How many degrees are there in the circle?
17:32360.
17:33Very basic information.
17:34If 360 degree has how many marks?
17:38It is given in the question.
17:40It is 540 marks.
17:43Total unitary method we are using.
17:45360 degrees means 540 marks.
17:48So what will be the value of 1 degree?
17:52When the value of more is given and 1 is subtracted, we always divide.
17:59Who should we divide with?
18:01Left hand side is 360, right hand side is 540.
18:05I want the value of 1 degree, so I have to divide left hand side by 1.
18:11If I divide both the sides by 360, is it becoming 1 degree?
18:22Yes.
18:23So 1 degree is how many marks?
18:25540 by 36.
18:280, 0 cancel.
18:31It is 54 by 36.
18:34Let me keep it as a fraction for now.
18:36You can also simplify it.
18:38Your answer will be same.
18:40Now let's find the marks of different subjects.
18:43I know the value of 1 degree and I want the value of different degrees.
18:48Please understand.
18:49If the cost of 1 pen is 10 rupees, what is the cost of 5 pen?
18:55It is 5 into 10, that is 50.
18:58We know the value of 1 and we want the value of more.
19:01We will always multiply.
19:03The value of 1 degree is how many marks?
19:08For example, I need to calculate how many marks in mathematics.
19:13What is the degree here?
19:1490 degree.
19:15If 1 degree is this much, then what will be 90 degree?
19:19So you just need to multiply this 90 degree by 54 upon 36.
19:26Are you getting it right?
19:27Total degrees, total circle is 360.
19:31Total value, total score is 540.
19:34360 degrees means 540.
19:37So what is the value of 1 degree?
19:39540 by 360.
19:40We have converted it to the fraction 54 by 36.
19:44We know the value of 1 degree.
19:46Now we will multiply it by the number of degrees required.
19:49So for maths, 90 into this number.
19:529 x 10 is 90.
19:549 x 4 is 36.
19:572 x 2 is 4.
19:592 x 2 is 4.
20:012 x 7 is 40.
20:042 x 5 is 10.
20:06So how much is left with me?
20:085 x 27.
20:10Let us do the calculation here.
20:127 x 5 is 35.
20:155 x 2 is 10.
20:173 x 3 is 13.
20:18Have a look.
20:19We have got 135 marks.
20:21So in mathematics, the child has scored 135 marks.
20:26Let us calculate for social studies now.
20:29We know that exactly the same process.
20:32What is the value of 1 degree?
20:3454 by 36.
20:36How many degrees do I need?
20:38I need to know for 65.
20:40So in social studies,
20:4265 degrees multiplied by the value of 1 degree.
20:4754 by 36.
20:49Let us see if this is divisible.
20:52Both are even numbers.
20:54Divisible by 2.
20:552 x 2 is 4.
20:572 x 7 is 14.
20:592 x 1 is 2.
21:002 x 8 is 60.
21:023 x 5 is 15.
21:043 x 6 is 18.
21:053 x 9 is 27.
21:07Once again.
21:083 x 2 is 6.
21:103 x 3 is 9.
21:11Now we will do what?
21:1365 x 3 divided by 2.
21:16Because 65 and 3 both are not divisible by 2.
21:19So first,
21:2065 x 3.
21:225 x 3 is 15.
21:246 x 3 is 18.
21:251 x 3 is 19.
21:27We have got the marks.
21:2865 x 3 is 195.
21:30But we have 2 in the denominator.
21:32Divide it by 2.
21:342 x 9 is 18.
21:37Difference is 1.
21:395 down.
21:402 x 7 is 14.
21:42Difference is 1.
21:44After that,
21:450 x 0 is 0.
21:472 x 5 is 10.
21:49So how many marks in social studies?
21:51It is 97.5.
21:53So value here is 97.5.
21:57Let us calculate for Hindi.
21:59Hindi's degree is what?
22:01Hindi's degree is 70 degrees.
22:03So if we know the value of 1 degree,
22:06and we have to find the value of 70,
22:08then what will we do?
22:10What we are doing repeatedly.
22:12We will multiply 70 by this number.
22:14So for Hindi,
22:16let us calculate.
22:1870 degrees multiplied by
22:2054 x 36.
22:23So this is
22:262 x 1 is 2.
22:282 x 8 is 16.
22:302 x 2 is 4.
22:31And 2 x 7 is 14.
22:339 x 2 is 18.
22:359 x 3 is 27.
22:3770 is divisible by 2.
22:39What is 70 divided by 2?
22:41It is 35.
22:43Now 35 x 3.
22:4535.
22:465 x 3 is 15.
22:483 x 3 is 9.
22:50And 1 x 10.
22:51What value did we get?
22:52105.
22:53So value here is 105.
22:55This is how you can calculate
22:57the marks in English.
22:5955 x this number.
23:01For science,
23:0280 x this number.
23:04Now,
23:06question was asking,
23:07in which subject did the student
23:09score 105 marks?
23:10Have we got in Hindi?
23:12So answer here for the first one is
23:14Hindi.
23:15In Hindi,
23:16the child has scored 105 marks.
23:18Second one.
23:20How many more marks were
23:22obtained by the student in Maths
23:24than in Hindi?
23:25Whenever there is a comparison,
23:27how many more,
23:28how many less,
23:29every time subtraction has to be done.
23:31Right?
23:32More doesn't mean addition every time.
23:34If I have scored 10 marks
23:36and you have scored 20 marks.
23:38So if I say,
23:39how many more marks you have scored?
23:41So you are not going to add 20 and 10.
23:43We will take the difference.
23:45So we need to find the difference
23:47of Maths and Hindi.
23:48What is the difference?
23:49105 and 135.
23:51The difference is of
23:5330 marks.
23:54What is the difference of both?
23:55Answer is 30.
23:57Third one.
23:58Examine means,
23:59check out,
24:00find out,
24:01whether the sum of the marks
24:03obtained in
24:05Social Science and Mathematics
24:07is more than
24:09in Science and Hindi.
24:11Now, we don't know the marks of Science.
24:13Let us find how many marks
24:15the child has scored in Science.
24:17What is the degree of Science?
24:1980.
24:20So what will we do of 80?
24:22For Science,
24:2380 has to be multiplied by
24:2554 upon 36.
24:289 x 4 is 36.
24:309 x 6 is 54.
24:334 x 2 is 8
24:35along with the 0.
24:37And 20 x 6 is 120.
24:40Okay?
24:41What is the score in Science?
24:43120.
24:44Question is asking you to check
24:46the sum of the marks
24:48obtained in Social Studies and Math.
24:50First, let us take Social Science and Math.
24:53135.0
24:5697.5
24:59This is Social Studies and Math.
25:020 plus 5 is 5.
25:047 plus 5 is 12.
25:069 plus 1 is 10.
25:08And 3 is 13.
25:101 and 1 is 2.
25:12So, total of these two subjects is
25:14232.5.
25:16Another combination is given for
25:18Science and Hindi.
25:20Okay?
25:21Science and Hindi.
25:23If we add these two,
25:25105 and
25:27125 to
25:30225.
25:31Question is asking,
25:32the sum of the marks obtained in
25:34Social Studies and Math is
25:36more than in Science and Hindi.
25:38Is this number more than 225?
25:41Answer is Yes.
25:42So, you need to write
25:44Yes here.
25:45Yes, the marks obtained in
25:47Social Studies and Math together
25:49are more than that of
25:51Science and Hindi together.
25:53Okay?
25:54I hope you are able to understand it well.
25:56I will just give you a quick recap
25:58once again,
25:59how you are going to go about
26:01the next of the questions.
26:03Okay.
26:04First of all,
26:05what you are going to do,
26:06you have to check,
26:07what is the
26:09total given for any particular child.
26:12Okay?
26:13Make the fraction.
26:15Fraction should be converted
26:17to degree.
26:18Now, how do we convert degree?
26:20Whatever is the value of
26:22fraction,
26:23multiply it by 360 degrees,
26:25you will get the degree.
26:27How do we convert degree?
26:29Son, if this is your
26:31circle graph.
26:32Okay?
26:33This is your circle.
26:34Suppose, you have to make
26:36120 degrees in it.
26:38You have your protector.
26:39Imagine, this is your protector.
26:41This is the whole protector.
26:42Here also, there is 0.
26:44180.
26:45Here also, there is 0.
26:46180.
26:47It is your choice.
26:48Whichever 0, you can pick.
26:49If I am starting the angle
26:51from here,
26:52I am opening the angle from here.
26:54You will forget the number above.
26:56You have to consider the number
26:580, 10, 20, 30.
26:59Okay?
27:000, 10, 20, 30.
27:01It will go till 90 here.
27:03100,
27:04110,
27:05120.
27:06Okay?
27:07You will mark 120 from the center.
27:09The whole angle is 120.
27:12After this,
27:13suppose, you have to make 85.
27:15Okay?
27:16What will you do?
27:17It is very easy.
27:19You can turn your notebook around.
27:22Turn around your notebook
27:24and consider as if
27:26Look.
27:27Consider as if this is a straight line.
27:29Okay?
27:30This is a straight line.
27:31And,
27:32your compass is lying somewhere here.
27:34Suppose, I have kept my compass here.
27:37It is very easy.
27:38I have kept my compass here.
27:39We have already made 120.
27:41Forget it.
27:42Now,
27:43turn around your notebook
27:44and consider
27:45this is your protector.
27:47Can't I make 85 here?
27:49Again,
27:50there is a 0 here
27:52and 180 here
27:53in your protector.
27:54Count from 0.
27:550, 10, 20, 30, 40, 50.
27:57It will go on.
27:5885 will be coming somewhere here.
28:01What will you do?
28:02Then,
28:03from center,
28:04mark a point here
28:06and that is 85 degrees.
28:08You will mark 85 degrees here.
28:11Okay?
28:12Now,
28:13suppose you want to make 60 degrees again.
28:15What should I do for 60 degrees?
28:17Right?
28:18Again,
28:19imagine.
28:20Let me just.
28:21Yes.
28:22Now,
28:23what will you do?
28:24Again,
28:25keep your protector here.
28:26I have already made this much.
28:27Consider your protector
28:28to be like this.
28:29Start from here.
28:31It is 180 from 0.
28:32Start measuring from 0.
28:3410, 20, 30, 40, 50, 60.
28:37Put a dot on 60 here
28:39and join it up.
28:40This angle is 60.
28:42In the similar manner,
28:43by rotating your notebook
28:45and adjusting the protector,
28:46you can easily measure the angles.
28:48Okay?
28:49This is all about the circle graph,
28:51pie chart or the circle chart.
28:54I hope you are able to understand
28:56how to formulate the percentages,
28:58degrees,
28:59how to show that.
29:00But please practice
29:01how to use the protector
29:03for marking these angles.
29:04That is a task.
29:05Okay?
29:06The more you make,
29:07the more you will get the confidence.
29:09So, thank you so very much
29:11for watching in
29:12and please don't forget
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29:14Thank you so much.