Mathematics
If the mean of the following distribution is 7.5, find the missing frequency f :
| Variable | Frequency |
|---|---|
| 5 | 20 |
| 6 | 17 |
| 7 | f |
| 8 | 10 |
| 9 | 8 |
| 10 | 6 |
| 11 | 7 |
| 12 | 6 |
Measures of Central Tendency
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Answer
| Variable (x) | Frequency (f) | fx |
|---|---|---|
| 5 | 20 | 100 |
| 6 | 17 | 102 |
| 7 | f | 7f |
| 8 | 10 | 80 |
| 9 | 8 | 72 |
| 10 | 6 | 60 |
| 11 | 7 | 77 |
| 12 | 6 | 72 |
| Total | ∑ f = 74 + f | ∑fx = 563 + 7f |
We know that,
n = ∑f = 74 + f.
By formula,
⇒ 7.5(74 + f) = 563 + 7f
⇒ 555 + 7.5f = 563 + 7f
⇒ 7.5f - 7f = 563 - 555
⇒ 0.5f = 8
⇒ f =
⇒ f = 16.
Hence, missing frequency f is 16.
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