Question
Find the missing frequency (p) for the following distribution whose mean is 7.68.
| x | 3 | 5 | 7 | 9 | 11 | 13 |
| f | 6 | 8 | 15 | P | 8 | 4 |
✓
Answer
| x | f | fx |
| 3 | 6 | 18 |
| 5 | 8 | 40 |
| 7 | 15 | 105 |
| 9 | P | 9P |
| 11 | 8 | 88 |
| 13 | 4 | 52 |
| N = P + 41 | $\sum\text{fx}=9\text{P}+303$ |
$\Rightarrow\text{Mean}=7.68$
$\Rightarrow\frac{\sum\text{fx}}{\text{N}}=68$
$\Rightarrow\frac{9\text{P}+303}{\text{P}+41}=7.68$
$\Rightarrow9\text{P}+303=\text{P}(7.68)+314.88$
$\Rightarrow9\text{P}-7.68\text{P}=314.88-303$
$\Rightarrow1.32\text{P}=11.88$
$\Rightarrow\text{P}=\frac{11.88}{1.32}$
$\Rightarrow\text{P}=9.$
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