Calculate the mean, median and the mode of the following numbers :

3, 1, 5, 6, 3, 4, 5, 3, 7, 2.

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

Sum of terms = 3 + 1 + 5 + 6 + 3 + 4 + 5 + 3 + 7 + 2 = 39

$\therefore \text{A.M.} = \dfrac{39}{10} = 3.9$

∴ Mean = 3.9

On arranging the numbers in ascending order we get,

1, 2, 3, 3, 3, 4, 5, 5, 6, 7.

Here, n (no. of observations) = 10, which is even.

$\therefore \text{Median} = \dfrac{\dfrac{n}{2} \text{th observation} + \big(\dfrac{n}{2} + 1\big)\text{ th observation}}{2} \\[1em] = \dfrac{\dfrac{10}{2} \text{th observation} + \big(\dfrac{10}{2} + 1\big)\text{ th observation}}{2} \\[1em] = \dfrac{\text{5th observation + 6th observation}}{2} \\[1em] = \dfrac{3 + 4}{2} \\[1em] = \dfrac{7}{2} \\[1em] = 3.5$

∴ Median = 3.5

In the given data : 3, 1, 5, 6, 3, 4, 5, 3, 7, 2.

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

∴ Mode = 3.

Hence, mean = 3.9, median = 3.5 and mode = 3.