Step 1: Determine the class midpoints ($x$) and sum of frequencies ($\sum f$). The given classes are 54-57, 58-61, 62-65, 66-69, 70-73, 74-77, 78-81, 82-85. The corresponding frequencies ($f$) are 5, 7, 10, 12, 6, 5, 4, 1. The midpoint ($x$) for each class is calculated as $\frac{\text{Lower Limit} + \text{Upper Limit}}{2}$. The total frequency is $\sum f = 5 + 7 + 10 + 12 + 6 + 5 + 4 + 1 = 50$. We will organize the calculations in a table: | Class Interval | Frequency ($f$) | Midpoint ($x$) | $fx$ | $|x - \bar{x}|$ | $f|x - \bar{x}|$ | $(x - \bar{x})^2$ | $f(x - \bar{x})^2$ | |:---------------|:----------------|:---------------|:-----|:----------------|:------------------|:------------------|:-------------------| | 54-57 | 5 | 55.5 | 277.5 | 11.44 | 57.20 | 130.8736 | 654.368 | | 58-61 | 7 | 59.5 | 416.5 | 7.44 | 52.08 | 55.3536 | 387.4752 | | 62-65 | 10 | 63.5 | 635.0 | 3.44 | 34.40 | 11.8336 | 118.336 | | 66-69 | 12 | 67.5 | 810.0 | 0.56 | 6.72 | 0.3136 | 3.7632 | | 70-73 | 6 | 71.5 | 429.0 | 4.56 | 27.36 | 20.7936 | 124.7616 | | 74-77 | 5 | 75.5 | 377.5 | 8.56 | 42.80 | 73.2736 | 366.368 | | 78-81 | 4 | 79.5 | 318.0 | 12.56 | 50.24 | 157.7536 | 631.0144 | | 82-85 | 1 | 83.5 | 83.5 | 16.56 | 16.56 | 274.2336 | 274.2336 | | Total | $\sum f = 50$ | | $\sum fx = 3347.0$ | | $\sum f|x - \bar{x}| = 287.36$ | | $\sum f(x - \bar{x})^2 =