Find the value of $p$, if the mean of the following distribution is 7.5.

| Classes | 2-4 | 4-6 | 6-8 | 8-10 | 10-12 | 12-14 |
|---|---|---|---|---|---|---|
| Frequency ($f_i$) | 6 | 8 | 15 | $p$ | 8

Question

Find the value of $p$, if the mean of the following distribution is 7.5.

| Classes | 2-4 | 4-6 | 6-8 | 8-10 | 10-12 | 12-14 |
|---|---|---|---|---|---|---|
| Frequency ($f_i$) | 6 | 8 | 15 | $p$ | 8 | 4 |

Accepted Answer

Step 1: Class marks ($x_i$): $3, 5, 7, 9, 11, 13$. $\sum f_i = 41 + p$. $\sum f_i x_i = 303 + 9p$
Step 2: Mean $= 7.5 = \frac{303 + 9p}{41 + p} \Rightarrow p = 3$

Question

Solution