Find the median of the following data: 41, 43, 127, 99, 61, 92, 71, 58, 57 if 58 replaced by 85, what will be the new median.
Answers
Given : Observations are : 41, 43, 127, 99, 61, 92, 71, 58, 57 if 58 replaced by 85.
Arranging given numbers in ascending order :
41, 43, 57, 58, 61, 71, 92, 99, 127
Number of observations, (n) = 9 (odd)
Median = value of (n + 1)/2)th observation
Median = value of (9 +1)/2 th observation
Median = value of (10)/2 th observation
Median = value of 5th observation
Median = 61
Median of the following data = 61
If 58 replaced by 85, then the new values are:
41, 43, 57, 61, 71, 85, 92, 99, 127
Therefore, n = 9 (odd)
Median = value of (n + 1)/2)th observation
New Median = value of (9 + 1)/2 th observation
New Median = value of (10)/2 th observation
New Median = value of 5th observation
New Median = 71
Hence the median of the following observations are 61 and the new median is 71.
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