Theory question 110
Measures of Central TendencyThe following table shows the distribution of test scores in a class.
Scores: 1, 2, 3, 4, 5, 7, 8, 9, 10
No. of Pupils: 1, 1, 5, 3, k2 + 1, 6, 2, 3, 4
(a) If the mean score of the class is 6, find the: (i) value of k; (ii) median score.
(b) Draw a bar chart for the distribution.
(c) If a pupil is picked at random from the class, what is the probability that he/she will score less than 6?
Show the model answer
(a)(i) Σf = k2 + 26; Σfx = 1 + 2 + 15 + 12 + 5(k2 + 1) + 42 + 16 + 27 + 40 = 5k2 + 160.
(5k2 + 160)/(k2 + 26) = 6 gives k2 = 4, so k = 2.
(ii) 30 pupils; median = average of 15th and 16th scores. Cumulative: 1, 2, 7, 10, 15 (score 5), 21 (score 7). Median = (5 + 7)/2 = 6.
(b) Bars of heights 1, 1, 5, 3, 5, 6, 2, 3, 4 above scores 1, 2, 3, 4, 5, 7, 8, 9, 10, with labelled axes.
(c) Scores below 6: 1 + 1 + 5 + 3 + 5 = 15 pupils. P = 15/30 = ½.
Set the mean formula equal to 6 and solve for k2.