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There are 10 observations arranged in ascending order as given below.

 45, 47, 50, 52, JC, JC + 2, 60, 62, 63, 74. The median of these observations is 53.

Find the value of JC. Also find the mean and the mode of the data.

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i. Given data in ascending order: 

45,47, 50, 52, x, JC+2, 60, 62, 63, 74. 

∴ Number of observations (n) = 10 (i.e., even) 

∴ Median is the average of middle two observations Here, the 5th and 6th numbers are in the middle position.

∴ 106 = 2x + 2 

∴ 106 – 2 = 2x 

∴ 104 = 2x 

∴ x = 52

∴ The given data becomes:

 45, 47, 50, 52, 52, 54, 60, 62, 63, 74

∴ The mean of the given data is 55.9.

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