Question

which statements about the box plot are correct? check all that apply. 0 25 50 75 100 125 fifty percent of the data values lies between 50 and 110. seventy - five percent of the data values lies between 20 and 50. it is unlikely that there are any outliers. the interquartile range is 25. the range is 78.

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box represents the inter - quartile range (IQR), where 50% of the data lies. The lower quartile ($Q_1$) is at the left - hand side of the box and the upper quartile ($Q_3$) is at the right - hand side of the box. The median is the line inside the box.

Step2: Analyze the first statement

The box in the given box - plot has $Q_1$ around 30 and $Q_3$ around 50. The range from 50 to 110 is not 50% of the data. So, the statement "Fifty percent of the data values lies between 50 and 110" is incorrect.

Step3: Analyze the second statement

Seventy - five percent of the data lies from the minimum value (around 20) to $Q_3$ (around 50). But the statement says "Seventy - five percent of the data values lies between 20 and 50", which is incorrect because 75% of the data is from the minimum value to $Q_3$, not just the range between 20 and 50.

Step4: Analyze the third statement

The whiskers of the box - plot extend quite far, which means there may be outliers. So, the statement "It is unlikely that there are any outliers" is incorrect.

Step5: Calculate the inter - quartile range

$Q_1\approx30$ and $Q_3\approx50$. The inter - quartile range $IQR = Q_3−Q_1=50 - 30=20
eq25$. So, the statement "The interquartile range is 25" is incorrect.

Step6: Calculate the range

The minimum value is around 20 and the maximum value is around 120. The range $R=\text{Max}-\text{Min}=120 - 20 = 100
eq78$. So, the statement "The range is 78" is incorrect.

Answer:

None of the statements are correct.