Page 256 - ICSE Math 7

(i) Mean:

x f fx

1 1 1

2 12 24 Mean = Σ fx = = 68 = 2.72
Σ
3 6 18 Σ f 25
4 5 20

5 1 5
25 68

n + 1
(ii) Median: Since n = 25 is odd, therefore median is the value of 2 th term, when
the data is arranged in ascending order.

1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 , 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5
n + 1 26
Now = = 13th term
2 2
∴ Median = 2
(iii) Mode: Since the highest frequency 12 corresponds to 2 chapattis. Therefore, the
mode is 2.
Now, let’s find the significance of each of the central tendencies in the above
situation. The mode of the data is 2 chapattis. If mode is used as the representative
value, then we need 50 chapattis, i.e., 2 each for 25 students. In this case almost
half of the students will remain hungry. The value of median is also 2, therefore
the same argument stands for median also. Moreover, mode and median are not
affected by extreme values, hence they are not useful in finding the total number of
chapattis required. The value of arithmetic mean is 2.72 which helps us to find the
total chapattis, i.e., 2.72 × 25 = 68. Thus, mean is the appropriate representative
value.

EXERCISE 22.1

1. The marks scored by 11 students in a Mathematics test are as follows:
34, 37, 30, 38, 50, 34, 34, 38, 36, 45, 31
Find the value of: (a) range (b) arithmetic mean (c) median (d) mode
2. The rainfall ‘in mm’ in a city over 7 days of a certain week is recorded as follows:

Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday

Rainfall 3.5 8.2 0.0 20.5 7.3 1.0 5.0

(a) Find the range of the amount of rainfall from the above data.

(b) Find the mean rainfall for the week.
(c) For how many days was the rainfall more than the average?

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