Theory question 109
Measures of DispersionThe weight (in kg) of 50 contestants at a competition is as follows:
65 66 67 66 64 66 65 63 65 68
64 62 66 64 67 65 64 66 65 67
65 67 66 64 65 64 66 65 64 65
66 65 64 65 63 63 67 65 63 64
66 64 68 65 63 65 64 67 66 64
(a) Construct a frequency table for the discrete data.
(b) Calculate, correct to 2 decimal places, the: (i) mean; (ii) standard deviation of the data.
Show the model answer
Model answer
(a) Weight: 62, 63, 64, 65, 66, 67, 68
Frequency: 1, 5, 12, 14, 10, 6, 2 (total 50)
(b)(i) Σfx = 3253, mean = 3253/50 = 65.06 kg
(ii) Σf(x − x̄)² = 92.82
SD = √(92.82/50) = √1.8564 ≈ 1.36 kg
Explanation
Multiply each squared deviation by its frequency before adding.