Theory question 105
Measures of DispersionThe table below gives the frequency distributions of marks obtained by some students in a scholarship examination.
Scores (x): 15, 25, 35, 45, 55, 65, 75
Freq. (f): 1, 4, 12, 24, 18, 8, 3
(a) Calculate, correct to 3 significant figures, the mean mark.
(b) Find the: (i) mode, (ii) range of the distribution.
Show the model answer
Model answer
(a) Σf = 70; Σfx = 15 + 100 + 420 + 1080 + 990 + 520 + 225 = 3350
Mean = 3350/70 = 47.86 ≈ 47.9
(b)(i) Mode = 45 (highest frequency, 24)
(ii) Range = 75 − 15 = 60
Explanation
Set out a column of fx; the mean is Σfx ÷ Σf.