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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.



Answer -

The weights (in kg) of 15 students are 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42 and 30.
Arranging them in ascending order, we have
27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45
Here, the number of observation , which is an odd number.
Hence, the median is
If the weights 44kg and 27kg are replaced by 46kg and 25kg respectively, then the given data becomes 31, 35, 25, 29, 32, 43, 37, 41, 34, 28, 36, 46, 45, 42 and 30.
Arranging the new data in ascending order, we have
25, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 45, 46
Here, the number of observation , which is an odd number.
Hence, the new median is

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