Question
Mathematics Question on frequency distributions
If the variance of the frequency distribution
| x i | Frequency f t |
|---|---|
| 2 | 3 |
| 3 | 6 |
| 4 | 16 |
| 5 | α |
| 6 | 9 |
| 7 | 5 |
| 8 | 6 |
is 3 , then α is equal to
Answer
The correct answer is 5.
| xi | fi | di=xi-5 | fidi2 | ffdf |
|---|---|---|---|---|
| 2 | 3 | -3 | 27 | -9 |
| 3 | 6 | -2 | 24 | -12 |
| 4 | 16 | -1 | 16 | -16 |
| 5 | α | 0 | 0 | 0 |
| 6 | 9 | 1 | 9 | 9 |
| 7 | 5 | 2 | 20 | 10 |
| 8 | 6 | 3 | 54 | 18 |
σx2=σd2=∑fi∑fidi2−(∑fi∑fidi)2
=45+α150−0=3
⇒150=135+3α
⇒3α=15⇒α=5