Theory question 114
StatisticsThe table gives the distribution of heights in metres of 100 students.
Height: 1.40 − 1.42, 1.43 − 1.45, 1.46 − 1.48, 1.49 − 1.51, 1.52 − 1.54, 1.55 − 1.57, 1.58 − 1.60, 1.61 − 1.63
Freq.: 2, 4, 19, 30, 24, 14, 6, 1
(a) Calculate the (i) mean height (ii) mean deviation of the distribution
(b) What is the probability that the height of a student selected at random is greater than the mean height of the distribution?
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Class marks 1.41, 1.44, 1.47, 1.50, 1.53, 1.56, 1.59, 1.62
(a)(i) Σfx = 151.23, mean = 151.23/100 ≈ 1.51 m (1.5123)
(ii) Σf|x − x̄| ≈ 3.333, mean deviation ≈ 3.333/100 ≈ 0.033 m
(b) The classes above the mean are 1.52 − 1.54 upwards: 24 + 14 + 6 + 1 = 45 students
Probability = 45/100 = 0.45
Use the class mark (middle value) of each class for x.