Question

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.

Answer 1

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,
$=\frac{\left(\frac{n}{2}\right)th\text{observation}+(\frac{n}{2}+1)th\text{observation}}{2}=\frac{\left(\frac{16}{2}\right)th\text{obseration}+(\frac{16}{2}+1)th\text{observation}}{2}$
$=\frac{8th\text{observation}+9th\text{observation}}{2}$
$=\frac{10+14}{2}=\frac{24}{2}=12$
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.