Theory question 108
Data PresentationThe ages, in years, of 50 teachers in a school are given below:
21 37 49 27 49 42 26 33 46 40
50 29 23 24 29 31 36 22 27 38
30 28 42 39 34 23 21 32 41 46
46 31 33 29 28 43 47 40 34 44
26 38 34 49 45 27 25 33 39 40
(a) Form a frequency distribution of the data using the intervals: 21 − 25, 26 − 30, 31 − 35, etc.
(b) Draw the histogram of the distribution.
(c) Use your histogram to estimate the mode.
(d) Calculate the mean age.
Show the model answer
(a) 21–25: 7; 26–30: 11; 31–35: 9; 36–40: 9; 41–45: 6; 46–50: 8 (total 50).
(b) Bars on class boundaries 20.5, 25.5, …, 50.5 with heights equal to the frequencies.
(c) Modal class 26–30. From the histogram (joining the corners of the tallest bar to the neighbouring bars): mode ≈ 25.5 + 5 × 4/(4 + 2) ≈ 28.8 years.
(d) Class marks 23, 28, 33, 38, 43, 48: Σfx = 161 + 308 + 297 + 342 + 258 + 384 = 1750. Mean = 1750/50 = 35 years.
Tally each age into its class first and check the frequencies add to 50.