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Question
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?
Solution
Given numbers are
46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33
Arrange in increasing order
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92
n =1(odd)
∴ Median = `((n+1)/2)^(th)value`
= `((11+1)/2)^(th)value`
= `6^(th) value = 58`
If 92 is replaced by 99 and 41 by 43
Then, the new values are
33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99
∴ n =11 (odd)
New median `((n+1)/2)^(th)`value
= `((11+1)/2)^(th)`value
= `6^(th)value`
= 58 .
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