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Answer :
The mean of the distribution, calculated from the given histogram, is approximately 44.66. The midpoint of each class and their frequencies were used to determine the mean.
To calculate the mean of a distribution from a histogram, we use the following formula:
Mean = Σ(Midpoint of each class * Frequency) / Total Frequency
Given the histogram:
Class Boundaries: 24.55, 29.45, 34.35, 39.25, 44.15, 49.05
Frequency: 5, 3, 1, 13.5, 46.5, 24.5
The midpoint of each class can be calculated as the average of the lower and upper class boundaries. So, the midpoints are:
Midpoint 1 = (24.55 + 29.45) / 2 = 27
Midpoint 2 = (29.45 + 34.35) / 2 = 31.9
Midpoint 3 = (34.35 + 39.25) / 2 = 36.8
Midpoint 4 = (39.25 + 44.15) / 2 = 41.7
Midpoint 5 = (44.15 + 49.05) / 2 = 46.6
Now, calculate the mean:
Mean = (27 * 5 + 31.9 * 3 + 36.8 * 1 + 41.7 * 13.5 + 46.6 * 46.5 + 49.05 * 24.5) / (5 + 3 + 1 + 13.5 + 46.5 + 24.5)
Mean ≈ (135 + 95.7 + 36.8 + 561.45 + 2163.9 + 1199.525) / 94
Mean ≈ 4192.475 / 94
Mean ≈ 44.66
Therefore, the mean of the distribution is approximately 44.66.
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