When computing the sum of scores from a grouped frequency distribution, which formula is used?

When computing the sum of scores from a grouped frequency distribution, which formula is used?

• A. Sum of the frequencies
• B. Sum of frequencies times the class midpoints
• C. Sum of the class midpoints
• D. Sum of frequencies squared times midpoints

Answer: (B)

When you want the total of all scores from a grouped frequency distribution, multiply each class’s frequency by its class midpoint and then add those products across all classes. This works because you don’t know the exact values within a class, so you approximate every observation in a class by the class midpoint. The product for that class estimates the total contribution of that class to the overall sum, and summing these estimates across all classes gives the approximate total score. For example, if a class has midpoint 4.5 with a frequency of 3, its contribution is 3 × 4.5 = 13.5. If another class has midpoint 14.5 with a frequency of 5, its contribution is 5 × 14.5 = 72.5. The total sum of scores would be 13.5 + 72.5 = 86.0. To get the mean, divide this by the total number of observations. Using only the sum of frequencies would give the total count, not the total score. Summing the class midpoints without accounting for how many observations are in each class ignores the distribution within classes. Squaring the frequencies and multiplying by midpoints isn’t a standard or meaningful approach for sums of scores.

When you want the total of all scores from a grouped frequency distribution, multiply each class’s frequency by its class midpoint and then add those products across all classes. This works because you don’t know the exact values within a class, so you approximate every observation in a class by the class midpoint. The product for that class estimates the total contribution of that class to the overall sum, and summing these estimates across all classes gives the approximate total score.

For example, if a class has midpoint 4.5 with a frequency of 3, its contribution is 3 × 4.5 = 13.5. If another class has midpoint 14.5 with a frequency of 5, its contribution is 5 × 14.5 = 72.5. The total sum of scores would be 13.5 + 72.5 = 86.0. To get the mean, divide this by the total number of observations.

Using only the sum of frequencies would give the total count, not the total score. Summing the class midpoints without accounting for how many observations are in each class ignores the distribution within classes. Squaring the frequencies and multiplying by midpoints isn’t a standard or meaningful approach for sums of scores.