Examples
Ex 1:
The median of the observations 11, 12, 14, 18, x + 2, x + 4, 30, 32, 35, 41 arranged in ascending order is 24. Find the value of x.
Sol:
Here, the number of observations n is 10. Since n is even.
Ex 2:
Find the mode and median of the following data:
12, 14, 12, 16, 15, 13, 14, 18, 19, 12, 14, 15, 16, 15, 16, 16, 15, 17, 13, 16, 16, 15, 15, 13, 15, 17, 15, 14, 15, 13, 15, 14.
Also, find the mean by using the empirical relation.
Sol:
Arranging the data in tabular form, we have
| Value | Tally bars | Frequency |
|---|---|---|
| 12 | ||| | 3 |
| 13 | |||| | 4 |
| 14 |  |
5 |
| 15 | |
10 |
| 16 | | |
6 |
| 17 | || | 2 |
| 18 | | | 1 |
| 19 | | | 1 |
| Total | 32 |
Looking at the table, we find that the value 15 occurs most frequently. So, 15 is the mode.
We find there are 32 observation i.e, n = 32.
| Hence, Median | = | 15 |
| Now, Mode | = | 3 Median – 2 Mean |
| ⇒ 15 | = | 3 × 15 – 2 Mean |
| ⇒ 2 Mean | = | 45 – 15 |
| ⇒ Mean | = | 30/2 |
| = | 15 | |
| Hence, Mean = Median = Mode = 15. | ||