The mean of the following frequency distribution is 18. The frequency $f$ in the class interval $19 - 21$ is missing. Determine $f$.

| Class interval | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 |

Question

The mean of the following frequency distribution is 18. The frequency $f$ in the class interval $19 - 21$ is missing. Determine $f$.

| Class interval | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 |
|---|---|---|---|---|---|---|---|
| Frequency | 3 | 6 | 9 | 13 | $f$ | 5 | 4 |

Accepted Answer

Step 1: Class marks ($x_i$): $12, 14, 16, 18, 20, 22, 24$. $\sum f_i = 40 + f$, $\sum f_i x_i = 704 + 20f$
Step 2: Mean $= \frac{\sum f_i x_i}{\sum f_i} \Rightarrow 18 = \frac{704 + 20f}{40 + f} \Rightarrow f = 8$

Question

Solution