Question

topic: measures of center
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
which of the following statements about the box - and - whisker plot below is true?
the midrange of the data set shown is 55.
there are more data points in the upper two quartiles than in the lower two quartiles.
the midrange of the data set shown is 85.
there are more data points inside the data box than are in the outside the data box.

Explanation:

Step1: Recall mid - range formula

The mid - range is calculated as $\frac{\text{Minimum}+\text{Maximum}}{2}$. From the box - and - whisker plot, the minimum value is 30 and the maximum value is 150.

Step2: Calculate mid - range

$\frac{30 + 150}{2}=\frac{180}{2}=90$. So the first and third options are wrong.

Step3: Understand quartile property

In a box - and - whisker plot, the number of data points in each quartile is the same. So the second option is wrong.

Step4: Understand data distribution in box

The box represents the inter - quartile range (IQR), which contains 50% of the data. The whiskers and outside points make up the other 50% of the data. So there are not more data points inside the box than outside.

Since none of the given statements are true, there may be an error in the problem setup. But if we focus on mid - range calculation:

Answer:

None of the above.