Question

Based on the relative frequency histogram below, which of the following statements is supported by the plot?

Answer 1

Answer: the IQR of the distribution is about 10

$IQR=Q_3-Q_1$

Q₃ class: (3/4)th value in cumulative frequency:

class 15-20

$Q_3=L+c\frac{0.75-cf}{f}=15+5\frac{0.75-0.85}{0.15}=15-3.33=11.67$

Q₁ class: (1/4)th value in cumulative frequency:

class 5-10

$Q_1=L+c\frac{0.25-cf}{f}=5+5\frac{0.25-0.5}{0.4}=5-3.125=1.875$

$IQR=11.67-1.875=9.795$