Question

Select all statements below that are true about the box plots shown.

1) The interquartile range for the cars going North is higher than the interquartile range for the cars going South.

2) The median speed for the cars going North is higher than the median speed for the cars going South.

3) The interquartile range for the cars going South is 9.

4) The interquartile range for the cars going North is 27.

5) The maximum speed for the cars going North is higher than the maximum speed for the cars going South.

6. The lower quartile for the cars going North is lower than the lower quartile for the cars going South.

Answer 1

Four and six . Because if you look at the graph

Answer 2

There are 4 Answers:

• Choice 1
• Choice 3
• Choice 5
• Choice 6

In other words, choices 2 and 4 are false while everything else is true.

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Step-by-step explanation:

The boxplot, or box-and-whisker plot, is a visual way to display a five number summary. Recall that the five items of a five number summary are:

1. Min
2. Q1
3. Median
4. Q3
5. Max

The min and max are exactly what they sound like: They're the smallest and largest values. Visually, this means they are the left and right most edges of the whiskers. This assumes that there are no outliers on either side.

The visual representation of Q1 and Q3 are the left and right edges of the box in that order. The gap between them is the IQR (interquartile range). The wider the box, the larger the IQR will be. The diagram shows the north cars have a larger IQR compared to the south ones.

Choice 1) is one of the answers since it is a true statement.

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The median is visually shown as a vertical line somewhere inside the box. It doesn't have to be at the exact midpoint of the left and right edges. We could have the median be closer to the left edge for instance, as the north cars boxplot shows.

Choice 2 is false because the diagram shows that the cars going south have a higher median speed, due to that lower vertical line being more to the right compared to the upper vertical line. In other words, the median speed of the cars going south is 64 mph while the median speed of the cars going north is 62 mph.

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Choice 3 is a bit tricky since the left edge of the blue box isn't lined up with a value on the number line. But it appears to be halfway between 58 and 60, so it seems like Q1 = 59 for the southbound cars. The value of Q3 for the southbound cars is Q3 = 68. The IQR is therefore,

IQR = Q3 - Q1 = 68-59 = 9

It's very likely that choice 3 is true

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For the northbound cars, we have

Q1 = 56

Q3 = 71 (assuming the right edge of the green box is exactly in the middle of the tickmarks of 70 and 72)

So,

IQR = Q3 - Q1 = 71 - 56 = 15

We don't get a result of 27, so choice 4 is not a true statement.

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Choice 5 is a true statement. The max speed of the northbound cars is larger than the max of the southbound cars. This is because the right tip of the north's whisker is further to the right compared to the south's corresponding whisker.

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The lower quartile is another name for "Q1" or "first quartile". So we'll be looking at the left edges of each box. The northbound cars have a smaller Q1 value because

Q1 = 56 for northbound cars

Q1 = 59 (or somewhere between 58 and 60) for southbound cars

Therefore, choice 6 is true.