The Marks of 10 Students of a Class in an Examination Arranged in Ascending Order is as Follows: - Mathematics

Sum

The marks of 10 students of a class in an examination arranged in ascending order are 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.

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

Since 46 has highest frequency.

Hence, the mode of the data is 46.

Concept: Concept of Median

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Chapter 24 Measure of Central Tendency(Mean, Median, Quartiles and Mode)
Exercise 24 (E) | Q 21 | Page 377

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