Exercise 5.1 Exercise 5.2 Exercise 5.3
Exercise 5.1
Question 1
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.
Sol :
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.
Question 2
The shoppers who come to a departmental store are marked as: man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning:
W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W W M W G W M G W M M B G G W
Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.
Sol :
By observing the data given above, we can make a frequency distribution table as follows.
Shopper | Tally marks | Number |
W |
| 28 |
M |
| 15 |
B | 5 | |
G |
| 12 |
The bar graph of this data can be drawn as follows.
Question 3
The weekly wages (in Rs) of 30 workers in a factory are.
830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840
Using tally marks make a frequency table with intervals as 800 − 810, 810 − 820 and so on.
Sol :
A frequency distribution table by using tally marks for the above data is as follows.
Interval | Tally marks | Frequency |
800 − 810 | 3 | |
810 − 820 | 2 | |
820 − 830 | 1 | |
830 − 840 |
| 9 |
840 − 850 | 5 | |
850 − 860 | 1 | |
860 − 870 | 3 | |
870 − 880 | 1 | |
880 − 890 | 1 | |
890 − 900 | 4 |
Question 4
Draw a histogram for the frequency table made for the data in Question 3 and answer the following questions.
(i) Which group has the maximum number of workers?
(ii) How many workers earn Rs 850 and more?
(iii) How many workers earn less than Rs 850?
Sol :
A histogram for the above frequency distribution table is as follows.
(i) 830 − 840 is the group which has the maximum number of workers.
(ii) The workers who earn more than Rs 850 are the number of workers who fall in the group of 850 − 860 or 860 − 870 or 870 − 880 or 880 − 890. Hence, the total number of workers earning more than 850 will be the sum of the numbers of all these workers i.e., 1 + 3 + 1 + 1 + 4 = 10
(iii) The workers who earn less than Rs 850 are the number of workers who fall in the group of 800 − 810 or 810 − 820 or 820 − 830 or 830 − 840 or 840 − 850. Hence, the total number of workers earning less than 850 will be the sum of the numbers of all these workers i.e., 3 + 2 + 1 + 9 + 5 = 20
Question 5
The number of hours for which students of a particular class watched television during holidays is shown through the given graph.
Answer the following
(i) For how many hours did the maximum number of students watch TV?
(ii) How many students watched TV for less than 4 hours?
(iii) How many students spent more than 5 hours in watching TV?
Sol :
(i) From the graph, it can be observed that the maximum number of students (i.e., 32) watched TV for 4 − 5 hours.
(ii) The students who watched TV for less than 4 hours are the students who watched TV for 1 − 2 hours or 2 − 3 hours or 3 − 4 hours.
Hence, total number of students = 4 + 8 + 22 = 34
(iii) The students who watched TV for more than 5 hours are the students who watched TV for 5 − 6 hours or 6 − 7 hours.
Hence, total number of students = 8 + 6 = 14