# 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.

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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.

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Given, numbers are:

31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30

Arrange in increasing order:

27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45

n = 15 (odd)

Therefore, median $=\frac{n+1}{2}$ value

$=\frac{15+1}{2}$

= 8th value = 35 kg

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)

Therefore, new median $=\frac{n+1}{2}$

$=\frac{15+1}{2}$

= 8th value = 35kg