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Question
Find the variance and standard deviation of the following scores on an exam: 92, 95, 85, 80, 75, 50.
Numerical
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Solution
Given scores: 92, 95, 85, 80, 75, 50
Step 1: Calculate Mean
`"Mean" = (92+95+85+75+50)/6`
= `477/6`
= 79.5
Step 2: Calculate Variance
`"Variance" = sum(x-barx)^2/n`
| Score | Deviation (x-79.5) | Square |
| 92 | 12.5 | 156.25 |
| 95 | 15.5 | 240.25 |
| 85 | 5.5 | 30.25 |
| 80 | 0.5 | 0.25 |
| 75 | -4.5 | 20.25 |
| 50 | -29.5 | 870.25 |
Sum of squares = 1317.5
Variance = `1317.5/6`
= 219.58
Step 3: Calculate Standard Deviation
Standard Deviation = `sqrt219.58`
= 14.82
- Variance = 219.58
- Standard Deviation = 14.82
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