Find the mean, median and mode of the following distribution :

8, 10, 7, 6, 10, 11, 6, 13, 10.

Arithmetic mean (A.M.) = $\dfrac{\text{Sum of terms}}{\text{No.of terms}} = \dfrac{∑x_i}{n}$

Sum of terms = 8 + 10 + 7 + 6 + 10 + 11 + 6 + 13 + 10 = 81.

$\therefore \text{A.M.} = \dfrac{81}{9} = 9.$

∴ Mean = 9.

On arranging the marks in ascending order, we get

6, 6, 7, 8, 10, 10, 10, 11, 13.

Here, n (no. of observations) = 9, which is odd.

$\therefore \text{Median} = \dfrac{n + 1}{2} \text{th observation} \\[1em] = \dfrac{9 + 1}{2} \\[1em] = \dfrac{10}{2} \\[1em] = 5 \text{th observation}$

5th observation = 10.

∴ Median = 10.

In the given data : 8, 10, 7, 6, 10, 11, 6, 13, 10

10 is repeated more number of times than any other number,

∴ Mode = 10.

Hence, mean = 9, median = 10 and mode = 10.