Page 254 - ICSE Math 7

Solution: Weight in kg (x ) Frequency (f ) x × f i
i
i
i
25 5 125
27 4 108
28 5 140

30 6 180

32 3 96
33 2 66
Sum ∑f = 25 ∑f x = 715
i
i i
∑x f 715
∴ mean = i i = = 28.6 kg
∑f i 25
Thus the mean weight = 28.6 kg

Median
The Median of a collection of data is the middle most value of the data when arranged in an order.
To find the median of the given data, first arrange the data in ascending or descending order and then
count the total number of observations ‘n’.
n + 1
If n is odd, Median = Value of th term
2
n n
1 th term
Value of c m th term + Value of c 2 + m
2
If n is even, Median =
2
Example 8: The heights of 6 students (in cm) are: 54, 52, 56, 54, 58, 51. Find the median.

Solution: On arranging the given data in ascending order, we get: 51, 52, 54, 54, 56, 58
Here, the number of observations n is 6 which is even.
n n
Value of 2 th term + Value of 2 + 1 th term
∴ Median =
2
6 6
Value of 2 th term + Value of 2 + 1 th term
=
2
3rd term + 4th term 56 + 54 110
= = = = 55
2 2 2
Median = 55 cm

Mode

Mode is value of the observation which occurs the maximum number of times in the data.
Let’s understand how to find mode and in which situations it is a relevant representative value of the data.
A group of students belonging to different classes are going for a trekking expedition. The organizers
are providing them with special shoes whose sizes are: 4, 5, 5, 5, 5, 5, 6, 6, 7, 9.
The average shoe size of 5.7 may not be appropriate for most of the students. The shoe size that fits
the maximum number of students is 5. Hence, the modal shoe size is worn by the maximum number
of students and is a true representative of the group.

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