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Question
The weights (in kg) of 15 students are: 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42,30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.
Solution
Given numbers are
31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30
Arranging increasing order
27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45
n = 15 (odd)
∴ Median = `((n+1)/2)^(th)`value
= `((15+1)/2)^(th)`value
= `8^(th)value`
= 35kg
If the weight 44kg is replaced by 46 kg and 27 kg is replaced by 25 kg
Then, new values in order be
25, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 45, 46
n =15 (odd)
∴ Median = `((n+1)/2)^(th)`value
= `((15+1)/2)^(th)`value
= `8^(th) value`
= 35kg
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