Theory question 113
Measures of DispersionIn a college, the number of absentees recorded over a period of 30 days was as shown in the frequency distribution table.
Number of absentees: 0–4, 5–9, 10–14, 15–19, 20–24
Number of days: 1, 5, 10, 9, 5
Calculate the: (a) mean; (b) standard deviation, correct to two decimal places.
Show the model answer
Model answer
Class marks x: 2, 7, 12, 17, 22; Σf = 30.
(a) Σfx = 2 + 35 + 120 + 153 + 110 = 420. Mean = 420/30 = 14.00.
(b) Deviations d = x − 14: −12, −7, −2, 3, 8. Σfd2 = 144 + 245 + 40 + 81 + 320 = 830.
SD = √(830/30) = √27.67 ≈ 5.26.
Explanation
Use the class mid-points as x.