Theory question 109
Measures of DispersionThe table shows the height of teak trees harvested by a farmer.
Height (m): 3, 4, 5, 6, 7, 8
Number of trees: 4, 6, 4, 5, 6, 2
(a) Find the median height.
(b) Calculate, correct to one decimal place, the: (i) mean; (ii) standard deviation.
Show the model answer
Model answer
(a) Σf = 27, so the median is the 14th value. Cumulative frequencies 4, 10, 14, … ⇒ median height = 5 m
(b)(i) Σfx = 12 + 24 + 20 + 30 + 42 + 16 = 144; mean = 144/27 ≈ 5.3 m
(ii) Σfx² = 834; variance = 834/27 − (144/27)² ≈ 2.444; standard deviation ≈ 1.6 m
Explanation
Find the position (n + 1)/2 for the median; use the exact mean for the standard deviation.