Question

The water bills (in ₹) of 25 houses in a certain locality for the period from January 1998 to March 1998 are given below:

56, 8, 5, 18, 10, 44, 50, 30, 47, 36, 25, 16, 14, 22, 20, 22, 30, 24, 15, 12, 27, 42, 45, 25, 24.

Construct a frequency table and cumulative frequency table.

Answer 1

Given:

Data (water bills in ₹) for 25 houses (Jan – Mar 1998): 56, 8, 5, 18, 10, 44, 50, 30, 47, 36, 25, 16, 14, 22, 20, 22, 30, 24, 15, 12, 27, 42, 45, 25, 24.

Step-wise calculation:

1. Sort the data in ascending order:

5, 8, 10, 12, 14, 15, 16, 18, 20, 22, 22, 24, 24, 25, 25, 27, 30, 30, 36, 42, 44, 45, 47, 50, 56

2. Count frequency of each distinct bill (tally and cumulative):

5 : frequency 1 → cumulative 1

8 : frequency 1 → cumulative 2

10 : frequency 1 → cumulative 3

12 : frequency 1 → cumulative 4

14 : frequency 1 → cumulative 5

15 : frequency 1 → cumulative 6

16 : frequency 1 → cumulative 7

18 : frequency 1 → cumulative 8

20 : frequency 1 → cumulative 9

22 : frequency 2 → cumulative 11

24 : frequency 2 → cumulative 13

25 : frequency 2 → cumulative 15

27 : frequency 1 → cumulative 16

30 : frequency 2 → cumulative 18

36 : frequency 1 → cumulative 19

42 : frequency 1 → cumulative 20

44 : frequency 1 → cumulative 21

45 : frequency 1 → cumulative 22

47 : frequency 1 → cumulative 23

50 : frequency 1 → cumulative 24

56 : frequency 1 → cumulative 25

A. Frequency table (distinct values) with cumulative frequency

Value	Frequency	Cumulative frequency
5	1	1
8	1	2
10	1	3
12	1	4
14	1	5
15	1	6
16	1	7
18	1	8
20	1	9
22	2	11
24	2	13
25	2	15
27	1	16
30	2	18
36	1	19
42	1	20
44	1	21
45	1	22
47	1	23
50	1	24
56	1	25

B. Grouped frequency table (useful for summary; class intervals of width 10)

Class	Frequency	Cumulative frequency
0 – 10	2	2
10 – 20	6	8
20 – 30	8	16
30 – 40	3	19
40 – 50	4	23
50 – 60	2	25