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.
