a) An estimate for the mean height of Chloe's classmates is 171.8 cm.
b) There is a difference between the actual mean and estimated mean because the actual mean considered all of the classmates in the population.
In order to determine an estimate for the mean height, we would first find the midpoint of the data set;
Height, h (cm) Frequency Midpoint Frequency × Midpoint
150 < h ≤ 160 3 (150+160)/2 = 155 155 × 3 = 465
160 < h ≤ 170 9 (160+170)/2 = 165 165 × 9 = 1485
170 < h ≤ 180 14 (170+180)/2 = 175 175 × 14 = 2450
180 < h ≤ 190 5 (180+190)/2 = 185 185 × 5 = 925
Estimated mean = (465 + 1485 + 2450 + 925)/(3 + 9 + 14 + 5)
Estimated mean = 5325/31
Estimated mean = 171.7742 ≈ 171.8 cm.
Part b.
There is a difference between the actual mean and estimated mean because the actual mean considered all of the classmates in the population while the estimated mean only considers a sample of the entire population.