QuestionAugust 25, 2025

(a) Find the midpoints for the classes. Class & Midpoint & Frequency 0.0-4.9 & square & 21 5.0-9.9 & square & 23 10.0-14.9 & square & 12 15.0-19.9 & square & 3 20.0-24.9 & square & 6 25.0-29.9 & square & 0 30.0-34.9 & square & 1 35.0-39.9 & square & 4 40.0-44.9 & square & 0 45.0-49.9 & square & 0 50.0-54.9 & square & 3

(a) Find the midpoints for the classes. Class & Midpoint & Frequency 0.0-4.9 & square & 21 5.0-9.9 & square & 23 10.0-14.9 & square & 12 15.0-19.9 & square & 3 20.0-24.9 & square & 6 25.0-29.9 & square & 0 30.0-34.9 & square & 1 35.0-39.9 & square & 4 40.0-44.9 & square & 0 45.0-49.9 & square & 0 50.0-54.9 & square & 3
(a) Find the midpoints for the classes. Class & Midpoint & Frequency 0.0-4.9 & square & 21 5.0-9.9 & square & 23 10.0-14.9 & square & 12 15.0-19.9 & square & 3 20.0-24.9 & square & 6 25.0-29.9 & square & 0 30.0-34.9 & square & 1 35.0-39.9 & square & 4 40.0-44.9 & square & 0 45.0-49.9 & square & 0 50.0-54.9 & square & 3

Solution
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Answer

2.45, 7.45, 12.45, 17.45, 22.45, 27.45, 32.45, 37.45, 42.45, 47.45, 52.45 Explanation 1. Calculate Midpoints The midpoint of a class is calculated using the formula: **Midpoint = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}**. Apply this to each class. - For 0.0-4.9: \frac{0.0 + 4.9}{2} = 2.45 - For 5.0-9.9: \frac{5.0 + 9.9}{2} = 7.45 - For 10.0-14.9: \frac{10.0 + 14.9}{2} = 12.45 - For 15.0-19.9: \frac{15.0 + 19.9}{2} = 17.45 - For 20.0-24.9: \frac{20.0 + 24.9}{2} = 22.45 - For 25.0-29.9: \frac{25.0 + 29.9}{2} = 27.45 - For 30.0-34.9: \frac{30.0 + 34.9}{2} = 32.45 - For 35.0-39.9: \frac{35.0 + 39.9}{2} = 37.45 - For 40.0-44.9: \frac{40.0 + 44.9}{2} = 42.45 - For 45.0-49.9: \frac{45.0 + 49.9}{2} = 47.45 - For 50.0-54.9: \frac{50.0 + 54.9}{2} = 52.45

Explanation

1. Calculate Midpoints<br /> The midpoint of a class is calculated using the formula: **Midpoint = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}**. Apply this to each class.<br /><br />- For 0.0-4.9: $\frac{0.0 + 4.9}{2} = 2.45$<br />- For 5.0-9.9: $\frac{5.0 + 9.9}{2} = 7.45$<br />- For 10.0-14.9: $\frac{10.0 + 14.9}{2} = 12.45$<br />- For 15.0-19.9: $\frac{15.0 + 19.9}{2} = 17.45$<br />- For 20.0-24.9: $\frac{20.0 + 24.9}{2} = 22.45$<br />- For 25.0-29.9: $\frac{25.0 + 29.9}{2} = 27.45$<br />- For 30.0-34.9: $\frac{30.0 + 34.9}{2} = 32.45$<br />- For 35.0-39.9: $\frac{35.0 + 39.9}{2} = 37.45$<br />- For 40.0-44.9: $\frac{40.0 + 44.9}{2} = 42.45$<br />- For 45.0-49.9: $\frac{45.0 + 49.9}{2} = 47.45$<br />- For 50.0-54.9: $\frac{50.0 + 54.9}{2} = 52.45$
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