Question

The marks of 10 students of a class in an examination arranged in ascending order is as follows:

13, 35, 43, 46, x, x + 4, 55, 61, 71, 80

If the median marks is 48, find the value of x. Hence, find the mode of the given data.

Answer 1

Data in ascending order:

13, 35, 43, 46, x, x + 4, 55, 61, 71, 80

Median = 48

Number of observations = n = 10  ...(Even)

∴ Median = `((n/2)^"th" "term" + (n/2 + 1)^"th" "term")/2`

`=> 48 = ((10/2)^"th" "term" + (10/2 + 1)^"th" "term")/2`

`=> 48 = (5^"th" "term" + 6^"th" "term")/2`

`=> 48 = (x + x + 4)/2`

`=> 48 = (2x + 4)/2`

`=>` 48 = x + 2

`=>` x = 46

`=>` x + 4 = 46 + 4 = 50

Thus, the observations are 13, 35, 43, 46, 46, 50, 55, 61, 71, 80

Since 46 has highest frequency.

Hence, the mode of the data is 46.