(b) The ages of the 5,000 primary school students surveyed was summarized and di
ID: 3045784 • Letter: #
Question
(b) The ages of the 5,000 primary school students surveyed was summarized and displayed in the box-and-whisker diagram shown overleaf in Exhibit 2.
Exhibit 2
Use the box-and-whisker diagram to:
(i) Determine the minimum and the maximum age of the students surveyed? (2 marks)
(ii) Determine the median age of the students surveyed. Interpret this value. (2 marks)
(iii) Comment on the skewness of this distribution. (2 marks)
(iv) Calculate the quartile deviation of the ages of the students surveyed. (2 marks)
Exhibit 2 7 10 12 13 Age of StudentsExplanation / Answer
Solution
(a) Minimum age = 6 years and maximum age = 12 years
(b) Median = 8 years
The median age is 8 years i.e. the mid-point of the data and is shown by the line that divides the box into two parts. Half the ages are greater than or equal to 8 years and half are less.
(c) The boxplot is right skewed
The ages are skewed right. The part of the box to the left of the median is shorter than the part to the right of the median.
(d) quartile deviation = (Q3-Q1)/2 = (10-7)/2 = 3/2 = 1.5
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