Page 245 - ICSE Math 6

that due to the extreme value ` 930, the average amount saved becomes more than double. Hence,
mean cannot be taken as a satisfactory central value for all types of data. So, for such data we need
a central tendency which does not get affected by the extreme values and, i.e., the median of a data.
The median of a data is the middle observation when all observations of the data are arranged in an
order.
The median of a data having n observations, all arranged in an order, is the:
n + 1
• th observation, if n is odd
2
n n
• mean of th observation and + 1 th observation, if n is even
2 2
Example 13: The ages (in years) of 7 men are given below.
45, 54, 28, 32, 65, 47, 35
Find the median of their ages.

Solution: The data when arranged in ascending order is: 28, 32, 35, 45, 47, 54, 65
7 + 1
th
Since n = 7 is an odd number, median is the th = 4 observation in 28, 32, 35,
45, 47, 54, 65, and i.e., 45. 2
Example 14: Find the median of 12, 14, 15, 11, 10, 8, 15, 14.
Solution: The data when arranged in ascending order is: 8, 10, 11, 12, 14, 14, 15, 15

Since the data has n = 8 observations and, i.e., even, therefore median is the mean of
n
n th observation and + 1 th observation.
2 2
n 8
th
th observation = th observation = 4 observation = 12
2 2
n 8
th
+ 1 th observation = + 1 th observation = 5 observation = 14
2 2
12 + 14
\ median = = 13
2
EXERCISE 22.3

1. The table shows the rainfall (in mm) in a city on 7 days of a certain week.

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 mean rainfall for the week.
(b) For how many days was the rainfall more than the average?
2. The marks scored by 10 students in a Mathematics test are as follows:
34, 37, 30, 38, 50, 34, 38, 34, 36, 45

Find the value of: (a) arithmetic mean (b) median
3. The weight (in kg) of ten students of a class are:
39, 42, 33, 45, 49, 40, 37, 44, 39, 44

Find the median weight.

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