Page 244 - ICSE Math 6

Arithmetic mean

The marks Sanskruti scored in 5 subjects are 60, 70, 70, 80 and 90. She tells her friends that her
average marks are 74. How did she reach this figure, inspite of the fact that she has not scored 74
marks in any of the subjects?

Let’s find the sum of the marks scored by Sanskruti in all the subject, Maths Info
i.e., 60 + 70 + 70 + 80 + 90 = 370. Now, if we divide this sum by the
370 The mean may or may not be
total number of subjects, i.e., 5, we get 5 = 74, which gives us the one of the observations in the
average marks. This average marks is the arithmetic mean or simply data.
the mean of the marks scored by Sanskruti. Thus, we conclude that arithmetic mean is defined as
the sum of all the observations of the data divided by the total number of observations.
Arithmetic mean of n observations x , x , x , ..., x is given by:
2
1
n
3
Mean = Sum of all observations = x 1 + x2 + x3 + ... + xn
Total number of observations n
Example 11: Pratibha studied for 3 hours, 4 hours, 7 hours and 2 hours on four consecutive days
before her final examination. How many hours did she study per day on an average?
Solution: The average time for which Pratibha studied during the four days is:
Total number of hours studied 3 + 4 + 7 + 2 16
= = = 4 hours
Number of days 4 4
Thus, Pratibha studied for 4 hours per day on an average.
Example 12: The heights, in inches, of 10 children are as follows:
41, 43, 44, 56, 38, 50, 48, 41, 44, 45

(a) What is the average height of children?
(b) How many children’s height is smaller than the average height?
th
(c) Find the new average height, if the height of 11 child is 67 inches?
Sum of heights
Solution: (a) Average height =
Total children
41 + 43 + 44 + 56 + 38 + 50 + 48 + 41 + 44 + 45 450
= 10 = 10
= 45 inches

(b) Five children’s height is smaller than the average height.
Sum of heights 450 + 67 517
(c) New average height = Total children = 10 + 1 = 11 = 47 inches

Thus, the new average height of 11 children is 47 inches.

Median
Consider the following data which gives the amount (in `) saved by
10 children. Maths Info
50, 10, 90, 30, 70, 10, 80, 70, 50, 40
The average amount saved by these 10 children is ` 50. Let’s add one The smallest and the largest
observations of a data are
more observation to this data, i.e., ` 930 saved by another child. Now, known as the extreme values.
the average amount saved by these 11 children is ` 130. We observe

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