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For which of these would you use a histogram to show the data?
(a) The number of letters for different areas in a postman’s bag.
(b) The height of competitors in an athletics meet.
(c) The number of cassettes produced by 5 companies.
(d) The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station.
Give reasons for each.
In case of the data given in alternative (b) and (d), we will use histogram as we can divide the given data in class intervals. In case of alternatives (a) and (c), we do not know about the number of letters of different areas and the number of cassettes produced by the given companies. We do not have any approximate idea about it. Therefore, we cannot define class intervals for this data and thus, we will not use a histogram.
A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer.
(i) Which season got the most votes?
(ii) Find the central angle of each sector.
(iii) Draw a pie chart to show this information.
|
Season |
Number of votes |
|
Summer |
90 |
|
Rainy |
120 |
|
Winter |
150 |
(i) Winter
(ii) Total number of votes = 90 + 120 + 150 = 360
|
Season |
Number of votes |
In fraction |
Central angle |
|
Summer |
90 |
|
|
|
Rainy |
120 |
|
|
|
Winter |
150 |
|
|
(iii) A pie chart can be drawn for the above data as follows.
Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.
|
Colours |
Number of people |
|
Blue |
18 |
|
Green |
9 |
|
Red |
6 |
|
Yellow |
3 |
|
Total |
36 |
The central angle for each colour can be calculated as follows.
|
Colours |
Number of people |
In fraction |
Central angle |
|
Blue |
18 |
|
|
|
Green |
9 |
|
|
|
Red |
6 |
|
|
|
Yellow |
3 |
|
|
The pie chart of the above data is as follows.
The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions.
(i) In which subject did the student score 105 marks?
(Hint: For 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?)
(ii) How many more marks were obtained by the student in Mathematics than in Hindi?
(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.
(Hint: Just study the central angles).
(i) Total marks obtained by the student are 540. Hence, 540 marks represent 360º. The central angle for 105 marks has to be calculated.
Central angle for 105 marks = 
Hindi is the subject having its central angle as 70º.
Therefore, the student scored 105 marks in Hindi.
(ii) Difference between the central angles of Mathematics and Hindi
= 90º − 70º = 20º
Marks for 20º central angle = 
There is a difference of 30 marks between the score obtained in Mathematics and Hindi.
Therefore, 30 more marks were obtained by the student in Mathematics than in Hindi.
(iii) Sum of central angles of Social Science and Mathematics
= 90° + 65° = 155°
Sum of central angles of Science and Hindi = 80° + 70° = 150°
The sum of the central angles for Social Science and Mathematics is more than that of Science and Hindi. Therefore, the student scored more in Social Science and Mathematics than in Science and Hindi.
The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.
|
Language |
Hindi |
English |
Marathi |
Tamil |
Bengali |
Total |
|
Number of students |
40 |
12 |
9 |
7 |
4 |
72 |
The central angle for each subject can be calculated as follows.
|
Language |
Number of students |
In fraction |
Central angle |
|
Hindi |
40 |
|
|
|
English |
12 |
|
|
|
Marathi |
9 |
|
|
|
Tamil |
7 |
|
|
|
Bengali |
4 |
|
|
A pie chart of the above data is as follows.
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