The standard deviation, s, is used to describe how spread out the data are and is calculated using the formula below. The mean is needed and was found to be x̄ = 67.
A table like the one below can be used to organize the observations, sample mean, deviations about the mean, and squared deviations about the mean. Fill in the missing values.
Observation xi | Sample Mean x̄ | Deviation About the Mean xi - x̄ | Squared Deviation About the Mean (xi - x̄)²
55 | 67 | -12 | 144
61 | 67 | -6 |
84 | 67 | | 289
74 | 67 | 7 | 49
70 | 67 | 3 | 9
73 | 67 | 6 | 36
18 | 67 | | 2,401
57 | 67 | | 100
78 | 67 | 11 | 121
79 | 67 | 12 | 144
81 | 67 | 14 |
74 | 67 | 7 | 49
| | | Σ (xi - x̄)² =