1. Calculate Population Variance `(sigma^2)` from the following mixed data
| Class | Frequency |
| 1 | 3 |
| 2 | 4 |
| 5 | 10 |
| 6 - 10 | 23 |
| 10 - 20 | 20 |
| 20 - 30 | 20 |
| 30 - 50 | 15 |
| 50 - 70 | 3 |
| 70 - 100 | 2 |
Solution:
Class
`(1)` | Frequency `(f)`
`(2)` | Mid value `(x)`
`(3)` | `f*x`
`(4)=(2)xx(3)` | `f*x^2=(f*x)xx(x)`
`(5)=(4)xx(3)` |
| 1 | 3 | 1 | 3 | 3 |
| 2 | 4 | 2 | 8 | 16 |
| 5 | 10 | 5 | 50 | 250 |
| 6 - 10 | 23 | 8 | 184 | 1472 |
| 10 - 20 | 20 | 15 | 300 | 4500 |
| 20 - 30 | 20 | 25 | 500 | 12500 |
| 30 - 50 | 15 | 40 | 600 | 24000 |
| 50 - 70 | 3 | 60 | 180 | 10800 |
| 70 - 100 | 2 | 85 | 170 | 14450 |
| --- | --- | --- | --- | --- |
| `n = 100` | ----- | `sum f*x=1995` | `sum f*x^2=67991` |
Mean `bar x = (sum fx)/n`
`=1995/100`
`=19.95`
Population Variance `sigma^2 = (sum f*x^2 - (sum f*x)^2/n)/n`
`=(67991 - (1995)^2/100)/100`
`=(67991 - 39800.25)/100`
`=28190.75/100`
`=281.9075`
2. Calculate Population Variance `(sigma^2)` from the following mixed data
| Class | Frequency |
| 2 | 1 |
| 3 | 2 |
| 4 | 2 |
| 5 - 9 | 8 |
| 10 - 14 | 15 |
| 15 - 19 | 8 |
| 20 - 29 | 4 |
Solution:
Class
`(1)` | Frequency `(f)`
`(2)` | Mid value `(x)`
`(3)` | `f*x`
`(4)=(2)xx(3)` | `f*x^2=(f*x)xx(x)`
`(5)=(4)xx(3)` |
| 2 | 1 | 2 | 2 | 4 |
| 3 | 2 | 3 | 6 | 18 |
| 4 | 2 | 4 | 8 | 32 |
| 5 - 9 | 8 | 7 | 56 | 392 |
| 10 - 14 | 15 | 12 | 180 | 2160 |
| 15 - 19 | 8 | 17 | 136 | 2312 |
| 20 - 29 | 4 | 24.5 | 98 | 2401 |
| --- | --- | --- | --- | --- |
| `n = 40` | ----- | `sum f*x=486` | `sum f*x^2=7319` |
Mean `bar x = (sum fx)/n`
`=486/40`
`=12.15`
Population Variance `sigma^2 = (sum f*x^2 - (sum f*x)^2/n)/n`
`=(7319 - (486)^2/40)/40`
`=(7319 - 5904.9)/40`
`=1414.1/40`
`=35.3525`
This material is intended as a summary. Use your textbook for detail explanation.
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