Question

6 the boxplot shows the monthly payments required to purchase a brand new car of two types: international & domestic. using the boxplots, select the correct statement. a 25% of the payments for the international cars were between $800 and $1600. b the interquartile range (iqr) for domestic is greater than the iqr for the international car payments. c the middle 50% of payments for international cars was between $400 and $600. d the distribution of domestic car payments is skewed to the right.

Explanation:

Step1: Recall Box - plot Properties

A box - plot (or box - and - whisker plot) shows the five - number summary: minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum. The inter - quartile range (IQR) is $IQR=Q_3 - Q_1$. The middle 50% of the data lies between $Q_1$ and $Q_3$.

Step2: Analyze Option A

For the international cars:
The first quartile ($Q_1$) is 400, the median ($Q_2$) is 600, and the third quartile ($Q_3$) is 800. The maximum is 1400.
The proportion of data between $Q_3$ (800) and the maximum (1400) is 25% (since the data is divided into four equal parts: 0 - 25% (min - $Q_1$), 25 - 50% ($Q_1$ - median), 50 - 75% (median - $Q_3$), 75 - 100% ($Q_3$ - max)). So, 25% of the payments for international cars were between $800$ and $1400$, not $1600$.

Step3: Analyze Option B

For domestic cars: Let's assume $Q_1 = 200$, $Q_3=400$, so $IQR_{domestic}=400 - 200=200$.
For international cars: $Q_1 = 400$, $Q_3 = 800$, so $IQR_{international}=800 - 400 = 400$.
Since $200<400$, the IQR for domestic is less than the IQR for international.

Step4: Analyze Option C

For international cars, $Q_1 = 400$ and $Q_3 = 800$. The middle 50% (the data between $Q_1$ and $Q_3$) of the payments for international cars was between $400$ and $800$, not $400$ and $600$ (the median is 600, which is the middle value of the entire data set, not the range of the middle 50%).

Step5: Analyze Option D

For a box - plot, if the whisker on the right side is longer than the whisker on the left side, the distribution is skewed to the right. For domestic cars, the whisker on the right side (from $Q_3 = 400$ to the maximum, say it's 600) is longer than the whisker on the left side (from the minimum, say it's 200 to $Q_1 = 200$).

Answer:

D. The distribution of Domestic car payments is skewed to the right.