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# 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. - ICSE Class 10 - Mathematics

ConceptMeasures of Central Tendency - Mean, Median, Mode for Raw and Arrayed Data

#### 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.

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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.
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