Question

The following observations have been arranged in ascending order. If the median of
the data is 63, find the value of x.
29, 32, 48, 50, X x+2, 72, 78, 84, 95​

Answer 1

Given:

29, 32, 48, 50, X x+2, 72, 78, 84, 95

• The number of observations, n = 10 (Even)

• Median = 63

To find out:

Find the value of x.

Formula used:

$\boxed{ Median = \frac{ (\frac{n}{2}) {}^{th} \: observation + ( \frac{n}{2} + 1) {}^{th} \: observation } {2} }$

Solution:

$Median = \frac{ (\frac{n}{2}) {}^{th} \: observation + ( \frac{n}{2}) {}^{th} \: observation}{2}$

$\rightarrow63 = \frac{( \frac{10}{2}) {}^{th} \: observation + ( \frac{10}{2} + 1) {}^{th} \: observation }{2}$

$\rightarrow63 = \frac{5 {}^{th} \: observation + {6}^{th} \: observation }{2}$

$\bigstar \: value \: of \: {5}^{th} \: obs. = x \: and \: {6}^{th} \: obs. = x + 2$

$\rightarrow \: 63 = \frac{x + x + 2}{2}$

$\rightarrow63 \times 2 = 2x + 2$

$\rightarrow126 = 2x + 2$

$\rightarrow2 x = 126 - 2$

$\rightarrow2x = 124$

$\rightarrow \: x = \frac{124}{4}$

$\rightarrow \: x = 62$

Hence, x = 62.

Answer 2

Given:

29,32,48,50,x,x + 2, 72,78,84,95

• The number of observation, n =10(Even)

• Median = 63

To find out:

find the value of x.

Formula used:

Median = (n/2)th observation + (n/2 + 1)th observation /2

Solutions:

Median = (n/2)th observation + (n/2)th observation /2

63 = (10/2)th observation + (10/2 + 1)th observation /2

63 = 5th observation + 6th observation /2

Value of 5th obs. = x and 6th obs. = x + 2

63 = x + x + 2 / 2

63 × 2 = 2x + 2

126 = 2x + 2

2x = 126 - 2

2x = 124

x = 62

Hence, x = 62.

silentlover45.❤️