Paper 1 · descriptive statistics / box plots
The times to the nearest minute taken by 12 students to complete a task are 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44, giving Q1 = 42, median = 44.5, and Q3 = 46.5 minutes (IQR = 4.5). The upper fence for outliers is Q3 + 1.5×IQR = 53.25 minutes. What can be concluded about the value 55 and the overall shape of the distribution?
A55 is below the upper fence, so it is not an outlier, and the distribution is symmetric
B55 exceeds the upper fence, so it is an outlier, and the distribution is positively skewed
C55 exceeds the upper fence, so it is an outlier, and the distribution is negatively skewed
D55 is below the upper fence, so it is not an outlier, and the distribution is positively skewed
Explanation: Since 55 > 53.25, it is an outlier. A high-side outlier pulls the tail of the distribution to the right, giving positive (right) skew.
Derived from ZIMSEC Statistics Paper 1, November 2020, Q2
