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Find the median of the following data:

$41, 43, 127, 99, 61, 92, 71, 58, 57 .$

If $58$ is replaced by $85$ , what will be the new median?

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Old mean = 61, New mean = 70

Old mean = 61, New mean = 71

Old mean = 50, New mean = 25

Old mean = 24, New mean = 63

answer is B.

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Detailed Solution

The given data is,

41, 43, 127, 99, 61, 92, 71, 58, 57

We need to find the new median if

58

is replaced by

85

.
We can arrange the given data in ascending order as shown below:

41, 43, 57, 58, 61, 71, 92, 99, 127

Total number of observations,

n = 9

When

n

is odd,

Median = (\frac{n + 1}{2})^{th} term

\Rightarrow Median = (\frac{9 + 1}{2})^{th} term

\Rightarrow Median = (\frac{10}{2})^{th} term

\Rightarrow Median = (5)^{th} term

\Rightarrow Median = 61

When

58

is replaced by

85

, the data can arranged as follows:

41, 43, 57, 61, 71, 85, 92, 99, 127

\Rightarrow New median = (5)^{th} term

\Rightarrow New median = 71

Thus the new median is

71

58

is replaced by

85

.
Hence, the correct option is 2.

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Find the median of the following data: 41,43,127,99,61,92,71,58,57.If 58 is replaced by 85, what will be the new median?

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Find the median of the following data:

$41, 43, 127, 99, 61, 92, 71, 58, 57 .$

If $58$ is replaced by $85$ , what will be the new median?