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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.
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 = (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.
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