Theory question 102
Data PresentationThe table below shows the weights, to the nearest kilogram, of twelve students in a Further Mathematics class.
Weight in kg: 55, 57, 59, 61, 63
Number of students: 2, 1, 2, 4, 3
(a) Draw a bar chart to illustrate the above information (b) What is (i) the mode (ii) the median of the distribution? (c) Calculate the mean weight, correct to the nearest kilogram.
Show the model answer
(a) Weights on the horizontal axis, number of students on the vertical axis; bars of equal width with heights 2, 1, 2, 4, 3; labelled axes and title.
(b)(i) Mode = 61 kg (highest frequency, 4).
(ii) In order the 12 weights are 55, 55, 57, 59, 59, 61, 61, 61, 61, 63, 63, 63; the 6th and 7th are both 61, so the median = 61 kg.
(c) Σfx = 110 + 57 + 118 + 244 + 189 = 718; Σf = 12.
Mean = 718 ÷ 12 = 59.83 ≈ 60 kg.
For the median of 12 values, average the 6th and 7th.