Find the median of the given data:

27, 9, 2, 35, 13, 7, 40, 20, 28, 22, 25, 24

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Question

Find the median of the given data:
27, 9, 2, 35, 13, 7, 40, 20, 28, 22, 25, 24

Lalit Mehra · Accepted Answer

Dear Student!

Total number of observation, n = 12(even)

The given observations can be arranged in ascending orders as 2, 7, 9, 13, 20, 22, 24, 25, 27, 28, 35, 40.

When number of observation, n is even, then

Median = Mean of $(\frac{n}{2})^{th}$ and $(\frac{n}{2} + 1)^{th}$ observations.

∴ Median = Mean of $(\frac{12}{2})^{th}$ and ${(\frac{12}{2} + 1)}^{th}$ observations

⇒ Median = Mean of 6^th and 7^th observations

6^th observation = 22 and 7^th observation = 24

∴ Median = Mean of 22 and 24 $= \frac{22 + 24}{2} = \frac{46}{2} = 23$

Thus, the median of the given observations is 23.

Cheers!

Find the median of the given data: 27, 9, 2, 35, 13, 7, 40, 20, 28, 22, 25, 24