The ages of children in a scout camp are 13,13,14,15,13,15,14,15,13,15 years. Find the mean, median and mode of the data.

For Mean:

Since, this is raw data. Mean is given by,

⇒

⇒

⇒ Mean = 14

Thus, mean of the data is 14.

For Median:

We need to arrange the raw data in ascending order. We have,

13, 13, 13, 13, 14, 14, 15, 15, 15, 15

Total number of items, n = 10 (even)

When n is even, then median is given by

…(i)

Calculate (n/2)^th position.

⇒

⇒

[∵ from the arranged data, 5^th term = 14] …(ii)

Now, calculate (n/2 + 1)^th position.

⇒

⇒

[∵ from the arranged data, 6^th term = 14] …(iii)

Putting (ii) and (iii) in equation (i), we get

Median = Mean of 14 and 14

⇒

⇒

⇒ Median = 14

Thus, median is 14.

For Mode:

We need to arrange the raw data in ascending order for ease of observation. We have,

13, 13, 13, 13, 14, 14, 15, 15, 15, 15

From observing from the arranged data, note that

13 → 4 times

14 → 2 times

15 → 4 times

Representing it in tabular form,

Highest frequency = 4

And the corresponding data are 13 and 15.

This is a bimodal distribution, because it has two modes.

Thus, modes are 13 and 15.