#### Question

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

13, 35, 43, 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.

#### Solution

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 = "5th term + 6th 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

Observation 46 is appearing twice.

Hence, the mode of the data is 46.

Is there an error in this question or solution?

#### APPEARS IN

Solution The Marks of 10 Students of a Class in an Examination Arranged in Ascending Order is as Follows: 13, 35, 43, 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. Concept: Measures of Central Tendency - Mean, Median, Mode for Raw and Arrayed Data.