GCEMathematicsStatistics2019

The table shows the frequency distribution of the heights (in cm) of 40 students. Height (cm): 150–154, 155–159, 160–164, 165–169 Frequency: 8, 14, 12, 6 Calculate the mean height of the students.

A157.5 cm
B158.0 cmCORRECT
C158.5 cm
D159.0 cm
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Why the answer is B, and why the others tempt you.
Using midpoints: 152, 157, 162, 167. Sum of (frequency × midpoint) = (8×152) + (14×157) + (12×162) + (6×167) = 1216 + 2198 + 1944 + 1002 = 6360. Mean = 6360 ÷ 40 = 159.0 cm. Recalculating: 8×152=1216, 14×157=2198, 12×162=1944, 6×167=1002; total=6360; mean=6360/40=159.0. Answer is D.
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