Finding the Mean of Grouped Data Worksheet

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For 11th grade statistics students. Complete each table to find the midpoint, the fx values, and the estimated mean. Round decimals to one decimal place when necessary.

Find the midpoint for each interval: (a) 0 to under 10, (b) 20 to under 40, (c) 15 to under 25.
A table shows two intervals: 0 to under 10 (frequency = 6) and 10 to under 20 (frequency = 4). Calculate the estimated mean.
Quiz scores are grouped: 10 to 19 (midpoint 14.5, f = 3), 20 to 29 (midpoint 24.5, f = 5), 30 to 39 (midpoint 34.5, f = 2). Find the sum of f and the sum of fx.
Using the previous quiz scores, calculate the estimated mean score.
Weekly study hours: 0-4 hours (f = 2), 5-9 hours (f = 7), 10-14 hours (f = 8), 15-19 hours (f = 3). Find the estimated mean. Use midpoints 2, 7, 12, 17.
Why can two datasets with the exact same grouped frequency table have different actual means?

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Finding the Mean of Grouped Data Worksheet

Answer key

Find the midpoint for each interval: (a) 0 to under 10, (b) 20 to under 40, (c) 15 to under 25.
(a) 5, (b) 30, (c) 20.
A table shows two intervals: 0 to under 10 (frequency = 6) and 10 to under 20 (frequency = 4). Calculate the estimated mean.
Midpoints are 5 and 15. Products are 5 * 6 = 30 and 15 * 4 = 60. Total fx = 90. Total frequency = 10. Estimated mean = 90 / 10 = 9.
Quiz scores are grouped: 10 to 19 (midpoint 14.5, f = 3), 20 to 29 (midpoint 24.5, f = 5), 30 to 39 (midpoint 34.5, f = 2). Find the sum of f and the sum of fx.
Total f = 3 + 5 + 2 = 10. Total fx = (14.5 * 3) + (24.5 * 5) + (34.5 * 2) = 43.5 + 122.5 + 69 = 235.
Using the previous quiz scores, calculate the estimated mean score.
Mean = 235 / 10 = 23.5.
Weekly study hours: 0-4 hours (f = 2), 5-9 hours (f = 7), 10-14 hours (f = 8), 15-19 hours (f = 3). Find the estimated mean. Use midpoints 2, 7, 12, 17.
Total fx = (2 * 2) + (7 * 7) + (12 * 8) + (17 * 3) = 4 + 49 + 96 + 51 = 200. Total f = 20. Estimated mean = 200 / 20 = 10 hours.
Why can two datasets with the exact same grouped frequency table have different actual means?
Because the exact original values within each interval are unknown. In one set, all values might cluster near the lower boundary, while in the other they might cluster near the upper boundary.