Question

The runs scored in a cricket match by 11 players are as follows:
6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 10
Find the mean, mode and median of this data.

Answer 1

Arranging the data in ascending order such that same values are put together, we get:

6,8,10,10,10,15,15,50,80,100,120.

Here, n = 11
∴ Median = Value of ${\left(\frac{n+1}{2}\right)}^{th}$ observation = Value of the 6^th observation = 15.
Here, 10 occurs three times. Therefore, 10 is the mode of the given data.
Now,
Mode = 3 Median - 2 Mean
⇒ 10 = 3 x 15 - 2 Mean
⇒2 Mean = 45 - 10 = 35
⇒ Mean = 35 $÷$ 2 = 17.5.