Question

a survey was conducted of 130 purchasers of new bmw 3 series cars, 130 purchasers of new bmw 5 series cars, and 130 purchasers of new bmw 7 series cars. in it, people were asked the age they were when they purchased their car. the following box plots display the results. part (a) in complete sentences, describe what the shape of each box plot implies about the distribution of the data collected for that car series. each box plot is spread out more in the ---select--- values. each plot is skewed to the ---select---, so the ages of the top 50% of buyers are ---select--- variable than the ages of the lower 50%.

Explanation:

To solve this, we analyze the box - plots:

Step 1: Analyze the spread direction

Looking at the box - plots, we observe that for each of the BMW car series (3, 5, and 7 series), the box and the whiskers extend more towards the higher values (the right - hand side of the number line which has higher age values like 40, 45, 50, etc.). So, each box plot is spread out more in the higher values.

Step 2: Analyze the skewness

In a box - plot, if the median (the dashed line inside the box) is closer to the lower end of the box, and the whisker on the higher side is longer, the distribution is skewed to the right. For all three box - plots, the median is closer to the left part of the box, and the right - hand whisker (representing the higher age values) is longer. So, each plot is skewed to the right.

Step 3: Analyze the spread of the top 50% and lower 50%

Since the distribution is skewed to the right, the top 50% of the data (the part of the data above the median) has a greater spread (more variability) than the lower 50% of the data (the part of the data below the median). This is because the right - hand side (top 50% in terms of age, since age is increasing to the right) has a longer whisker and the box is also more spread out on the right.

Answer:

First "---Select---": higher
Second "---Select---": right
Third "---Select---": more spread out (or have more variability)