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Ten observations 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34, 43 are written in an ascending order. The median of the data is 24. Find the value of x.

Solution:

Given, ten observations are written in an ascending order.

The observations are 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34, 43

The median of the data is 24

We have to find the value of x.

Total number of observations, n = 10

Here, n is even

The formula for median when n is even is given by

Median = [(n/2)^th observation + ((n/2) + 1)^th observation] / 2

So, median = [(10/2)^th observation + ((10/2) + 1)^th observation] / 2

24 = [5^th observation + (5 + 1)^th observation] / 2

24 = [5^th observation + 6^th observation] / 2

24 = [(x + 1) + (2x - 13)]/2

48 = x + 2x + 1 - 13

48 = 3x - 12

3x = 48 + 12

3x = 60

x = 60/3

x = 20

Therefore, the value of x is 20.

✦ Try This: Calculate the mean deviation from the mean for the following data: 57, 64, 43, 67, 49, 59, 44, 47, 61, 59

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14

NCERT Exemplar Class 9 Maths Exercise 14.3 Problem 13

Summary:

Ten observations 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34, 43 are written in an ascending order. The median of the data is 24. The value of x is 20

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