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.

Answer 1

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.