Statistics Question 8
Question 8 - 2024 (30 Jan Shift 2)
The variance $\sigma^{2}$ of the data
| $x _i$ | 0 | 1 | 5 | 6 | 10 | 12 | 17 |
|---|---|---|---|---|---|---|---|
| $f _i$ | 3 | 2 | 3 | 2 | 6 | 3 | 3 |
Is
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Answer (29)
Solution
| $x _i$ | $f _i$ | $f _i x _i$ | $f _i x _i{ }^{2}$ |
|---|---|---|---|
| 0 | 3 | 0 | 0 |
| 1 | 2 | 2 | 2 |
| 5 | 3 | 15 | 75 |
| 6 | 2 | 12 | 72 |
| 10 | 6 | 60 | 600 |
| 12 | 3 | 36 | 432 |
| 17 | 3 | 51 | 867 |
| $\sum f _i=22$ | $\sum f _i x _i{ }^{2}=2048$ |
$\therefore \quad \sum f _i x _i=176$
So $\overline{x}=\frac{\sum f _i x _i}{\sum f _i}=\frac{176}{22}=8$
for $\sigma^{2}=\frac{1}{N} \sum f _i x _i^{2}-(\overline{x})^{2}$
$=\frac{1}{22} \times 2048-(8)^{2}$
$=93.090964$
$=29.0909$
