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Question
The median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54, 84 is ______.
Options
45
49.5
54
56
Solution
The median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54, 84 is 54.
Explanation:
First, we arrange the given observations in ascending order as follows:
22, 34, 39, 45, 54, 54, 56, 68, 78 and 84
Here, total number of observations, n = 10
Since, n is even, so we use the formula for median,
Median = `((n/2)"th observation" + (n/2 + 1)"th observation")/2`
= `((10/2)"th observation" + (10/2 + 1)"th observation")/2` ...[Put n = 10]
= `(5"th observation" + 6"th observation")/2`
= `(54 + 54)/2`
= `108/2`
= 54
Hence, the median of given data is 54.
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