Theory question 111
Measures of Central TendencyThe table shows the age distributions of the members of a club.
Age (years): 10-14, 15-19, 20-24, 25-29, 30-34, 35-39
Frequency: 7, 18, 25, 17, 9, 4
(a) Calculate, correct to one decimal place, the mean age. (b)(i) Draw a histogram to illustrate the information (ii) Use the histogram to estimate the modal age. (c) If a member is selected at random, what is the probability that he/she is in the modal class?
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(a) Class marks 12, 17, 22, 27, 32, 37; Σf = 80; Σfx = 84 + 306 + 550 + 459 + 288 + 148 = 1835. Mean = 1835/80 ≈ 22.9 years.
(b)(i) Bars on boundaries 9.5, 14.5, …, 39.5 with heights 7, 18, 25, 17, 9, 4.
(ii) In the tallest bar join its top corners to the neighbouring bars' tops; they cross at about 19.5 + 7/15 × 5 ≈ 21.8 years.
(c) Modal class 20–24 has 25 members: P = 25/80 = 5/16.
Use the class mid-points for x when finding the mean.