Find the median of the following observations: 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?
Answers
Given : Observations are : 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data.
Arranging given numbers in ascending order :
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92
Number of observations, (n) = 11 (odd)
Median = value of (n +1)/2)th observation
Median = value of (11 +1)/2 th observation
Median = value of (12)/2 th observation
Median = value of 6th observation
Median = 58
If 92 is replaced by 99 and 41 by 43, then the new values are:
33, 35, 43, 46, 55, 58, 64, 77, 81, 90, 99
Therefore, n = 11 (odd)
Median = value of (n +1)/2)th observation
New Median = value of (11 +1)/2 th observation
New Median = value of (12)/2 th observation
New Median = value of 6th observation
New Median = 58
Hence the median of the following observations are 58 and the new median is 58.
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