Theory question 105
Measures of Central TendencyThe data represent the scores obtained by 9 applicants in an interview arranged in ascending order: (3x + 2), 22, (4x − 2), 23, 25, (5x − 4), 29, 29 and (x2 − 7). (a) Given that the range is 9, find the: (i) value of x; (ii) mean mark of the applicants. (b) If four of the applicants who obtained the highest score were selected, determine the pass mark.
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Model answer
(a)(i) Range: (x² − 7) − (3x + 2) = 9 ⇒ x² − 3x − 18 = 0 ⇒ (x − 6)(x + 3) = 0; x = −3 would make the first score negative, so x = 6
Scores: 20, 22, 22, 23, 25, 26, 29, 29, 29
(ii) Mean = 225 ÷ 9 = 25
(b) The four highest scores are 29, 29, 29 and 26, so the pass mark is 26
Explanation
Substitute x back in and check the list is in ascending order.