Theory question 107
Data PresentationThe number of child births recorded in 50 maternity centres of a local government in August 1993 are as follows:
50 99 81 86 69 85 93 63 92 65
77 74 76 71 90 74 81 94 67 75
95 81 68 105 99 68 75 75 76 73
79 74 80 69 74 62 74 80 79 68
79 75 75 71 83 75 80 85 81 82
(a) Construct a frequency distribution table, using class intervals 45–54, 55–64, etc. (b) Draw the histogram for the distribution. (c) Use your histogram to estimate the mode. (d) Calculate the mean number of births.
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(a) 45–54: 1; 55–64: 2; 65–74: 15; 75–84: 21; 85–94: 7; 95–104: 3; 105–114: 1 (total 50).
(b) Bars on class boundaries 44.5, 54.5, … 114.5 with heights equal to the frequencies.
(c) In the tallest bar (74.5–84.5) join its top corners to the neighbouring bars' tops; the lines cross at about 77.5, so the mode ≈ 77.5.
(d) Class marks 49.5, 59.5, … 109.5: Σfx = 49.5 + 119 + 1042.5 + 1669.5 + 626.5 + 298.5 + 109.5 = 3915. Mean = 3915/50 = 78.3.
Tally the data one class at a time and check the frequencies add to 50.