Answer:
To find the mean of the frequency distribution, we need to calculate the weighted average of the values and their corresponding frequencies.
First, let's list the midpoints of each class interval:
Midpoint of 0-4: (0 + 4) / 2 = 2
Midpoint of 5-9: (5 + 9) / 2 = 7
Midpoint of 10-14: (10 + 14) / 2 = 12
Midpoint of 15-19: (15 + 19) / 2 = 17
Midpoint of 20-24: (20 + 24) / 2 = 22
Midpoint of 25-29: (25 + 29) / 2 = 27
Next, let's calculate the sum of the products of each midpoint and its corresponding frequency:
(2 * 3) + (7 * 4) + (12 * 5) + (17 * 4) + (22 * 3) + (27 * 1) = 6 + 28 + 60 + 68 + 66 + 27 = 255
Finally, let's calculate the sum of the frequencies:
3 + 4 + 5 + 4 + 3 + 1 = 20
To find the mean, we divide the sum of the products by the sum of the frequencies:
Mean = 255 / 20 = 12.75
Therefore, the mean of the frequency distribution is 12.75.