**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.**

**Solution: **

(b) The height of competitors in an athletics meet.

(d) The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station.

Reason:Histogram is a graphical representation of data when the data is represented using the class-interval, where class-interval is the numerical width of any class.

As the cases mentioned in the options (b) and (d) data can be divided into class-intervals, therefore histogram can be used for representing the data.

Whereas in the cases (a) and (c) the data can’t be divided into class-intervals, thus histogram can’t be used for representing the data.

**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.**

**Solution: **

Frequency distribution table using tally marks:

The bar graph to illustrate data:

**Question 3. The weekly wages (in ₹) 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.**

**Solution:**

Frequency table with intervals as 800–810, 810–820 and so on using tally marks are given below:

**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 ₹850 and more?**

**(iii) How many workers earn less than ₹ 850?**

**Solution: **

(i)Group 830-840 has the maximum number of workers working, i.e., 9.

Reason:When seeing the graph we can observe that group having weekly wage 830-840 there are 9 workers working.

(ii)10 workers earn more than or equal to ₹ 850.

Reason:When seeing the graph we can observe that group having weekly wage more than or equal to ₹ 850, there are 10 workers working when we add all the workers having wage more than or equal to ₹ 850.

(iii)20 workers earn less than ₹ 850.

Reason:When seeing the graph we can observe that group having weekly wage less than ₹ 850, there are 20 workers working when we add all the workers having wage less than ₹ 850.

**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?**

**Solution: **

(i)By observing the graph we can find that the maximum number of students i.e. 32 watched TV for 4 to 5 hours.

(ii)The students who watched TV for less than 4 hours are 34 students.

Reason:Students who watch TV for 1-2 hours : 4

Students who watch TV for 2-3 hours : 8

Students who watch TV for 3-4 hours : 22

Therefore, the student who watched TV for less than 4 hours are 4+8+22 = 34

(iii)The students who watched TV for more than 5 hours are 14 students.

Reason:Students who watch TV for 6-6 hours : 8

Students who watch TV for 6-7 hours : 6

Therefor the student who watched TV for more than 5 hours are 8+6 = 14