Theory question 106
StatisticsThe table shows the distribution of ages of 22 students in a school.
Age (years): 12 − 14, 15 − 17, 18 − 20, 21 − 23, 24 − 26
Freq.: 6, 10, 3, 2, 1
Using an assumed mean of 19, calculate, correct to three significant figures, the: (a) mean age; (b) standard deviation of the distribution.
Show the model answer
Model answer
Class marks 13, 16, 19, 22, 25; d = x − 19 = −6, −3, 0, 3, 6.
Σfd = −36 − 30 + 0 + 6 + 6 = −54; Σfd² = 216 + 90 + 0 + 18 + 36 = 360.
(a) Mean = 19 + (−54/22) = 16.5 years (16.545).
(b) SD = √(360/22 − (54/22)²) = √(16.364 − 6.025) = √10.339 = 3.22.
Explanation
Use class marks and the coded deviations d = x − 19.