Theory question 109
Data PresentationThe table below gives the ages, to the nearest 5 years, of 50 people.
Age in years: 10, 15, 20, 25, 30
No. of People: 8, 19, 10, 7, 6
(a) Construct a cumumlative frequency table for the distribution. (b) Draw a cumulative frequency curve (ogive). (c) From your ogive, find the: (i) median age: (ii) number of people who are at most 15 years of age. (iii) number of people who are between 20 and 25 years of age.
Show the model answer
(a) Upper class boundaries 12.5, 17.5, 22.5, 27.5, 32.5 with cumulative frequencies 8, 27, 37, 44, 50
(b) Plot cumulative frequency against upper class boundary (start at (7.5, 0)) and join with a smooth S-shaped curve.
(c)(i) Median at the 25th person: about 17 years (12.5 + 17/19 × 5 ≈ 17.0)
(ii) At most 15 years (read at 17.5): 27 people
(iii) Read the curve at 20 and 25 years (about 32 and 40): about 8 people
Ages 'to the nearest 5 years' mean each class spans 2.5 years either side, so plot at upper class boundaries.