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Question
There are 10 observations arranged in ascending order as given below. 45, 47, 50, 52, x, x + 2, 60, 62, 63, 74. The median of these observations is 53. Find the value of x. Also find the mean and the mode of the data.
Solution
The 10 observations are arranged in ascending order as given below.
45, 47, 50, 52, x, x + 2, 60 ,62 ,63 ,74.
Since, the number of observations is 10, which is an even number.
∴ 5th 6th and two such numbers mark in the middle. They are x + x + 2 respectively.
The median of the given observations is 53.
∴ Median = `(x + x + 2)/2`
∴ 53 = `(2x + 2)/2`
∴ 53 × 2 = 2x + 2
∴ 106 = 2x + 2
∴ 104 = 2x
∴ x = `104/2`
∴ x = 52
Given data = 45, 47, 50, 52, 52, 54, 60, 62, 63, 74.
∴ Mean = `"Sum of all observations"/"Total number of all observations "`
`(45+47+50+52+52+54+60+62+63+74)/10`
= `559/10`
∴ Mean = 55.9
Since, the observation that is occurring the maximum is 52.
So, the mode of the data is 52.
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