Question

Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14
By using the empirical relation also find the mean.

Answer 1

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

12,12,13,13, 14,14,14, 16, 19
Here, n = 9.
∴ Median = Value of ${\left(\frac{n+1}{2}\right)}^{th}$ observation = Value of the 5^th observation = 14.
Here, 14 occurs the maximum number of times, i.e., three times. Therefore, 14 is the mode of the data.

Now,
Mode = 3 Median - 2 Mean
$\Rightarrow$ 14 = 3 x 14 - 2 Mean
$\Rightarrow$2 Mean = 42 - 14 = 28
$\Rightarrow$ Mean = 28 $÷$ 2 = 14.