Question 14
The points scored by a basketball team in a series of matches are as follows.
17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28
Find the median and mode of the data.

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Solution

First, arrange the given points scored in ascending order.
2, 5, 7, 7, 8, 10, 10, 10, 14, 17, 18, 24, 25, 27, 28, 48
Here, number of observations, n = 16 (even)
Since n is even, we use the formula for median,
$= \frac{(\frac{n}{2}) t h o b s e r v a t i o n + (\frac{n}{2} + 1) t h o b s e r v a t i o n}{2} = \frac{(\frac{16}{2}) t h o b s e r a t i o n + (\frac{16}{2} + 1) t h o b s e r v a t i o n}{2}$
$= \frac{8 t h o b s e r v a t i o n + 9 t h o b s e r v a t i o n}{2}$
$= \frac{10 + 14}{2} = \frac{24}{2} = 12$
We know that, mode is the observation which is repeated maximum number of times.
In the given data, 10 is repeated 3 times.
So, mode of the given data is 10.
Hence, median and mode for the given data are 12 and 10 respectively.

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