Question 3.19: Comparison of Outdoor Paint Find the variance and standard d......
Comparison of Outdoor Paint
Find the variance and standard deviation for brand B paint data in Example 3–15. The months brand B lasted before fading were
35, 45, 30, 35, 40, 25
Step 1 Find the mean.
\mu = \frac{ΣX}{N} = \frac{35 + 45 + 30 + 35 + 40 + 25}{6} = \frac{210}{6} = 35
Step 2 Subtract the mean from each value, and place the result in column B of the table.
35 − 35 = 0 45 − 35 = 10 30 − 35 = −5
35 − 35 = 0 40 − 35 = 5 25 − 35 = −10
Step 3 Square each result and place the squares in column C of the table.
Step 4 Find the sum of the squares in column C.
Σ(X − μ)² = 0 + 100 + 25 + 0 + 25 + 100 = 250
Step 5 Divide the sum by N to get the variance.
\sigma^2=\frac{\Sigma(X-\mu)^2}{N}=\frac{250}{6}=41.7
Step 6 Take the square root to get the standard deviation.
\sigma=\sqrt{\frac{\Sigma(X-\mu)^2}{N}}=\sqrt{41.7} \approx 6.5
Hence, the standard deviation is 6.5.
| A | B | C |
| X | X − μ | (X − μ)² |
| 35 | 0 | 0 |
| 45 | 10 | 100 |
| 30 | -5 | 25 |
| 35 | 0 | 0 |
| 40 | 5 | 25 |
| 25 | -10 | 100 |