Theory question 111
Measures of DispersionThe table shows the distribution of the number of hours per day spent in studying by 50 students.
Number of hours per day: 4, 5, 6, 7, 8, 9, 10, 11
Number of students: 5, 7, 5, 9, 12, 4, 3, 5
Calculate, correct to two decimal places, the: (a) mean; (b) standard deviation.
Show the model answer
Model answer
(a) Σfx = 20 + 35 + 30 + 63 + 96 + 36 + 30 + 55 = 365
Mean = 365/50 = 7.30
(b) Σfx2 = 2873; variance = 2873/50 − 7.32 = 57.46 − 53.29 = 4.17
Standard deviation = √4.17 ≈ 2.04
Explanation
Use either Σf(x − mean)2 or Σfx2/Σf − mean2; both give 4.17.