which statements about the box plot are correct? check all that apply. \nfifty percent of the data values…

which statements about the box plot are correct? check all that apply. \nfifty percent of the data values lies between 34 and 46.\nseventy - five percent of the data values lies between 42 and 70.\nit is unlikely that there are any outliers.\nthe interquartile range is 24.\nthe range is 36.

which statements about the box plot are correct? check all that apply. \nfifty percent of the data values lies between 34 and 46.\nseventy - five percent of the data values lies between 42 and 70.\nit is unlikely that there are any outliers.\nthe interquartile range is 24.\nthe range is 36.

Answer

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box represents the inter - quartile range (IQR), which contains 50% of the data. 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. The range is the difference between the maximum and minimum values, and outliers are points outside the whiskers.

Step2: Analyze the first statement

If 50% of the data lies between two values, these values should be $Q_1$ and $Q_3$. From the box - plot, assume $Q_1 = 42$ and $Q_3=66$. The statement "Fifty percent of the data values lies between 34 and 46" is incorrect.

Step3: Analyze the second statement

75% of the data lies between the minimum value and $Q_3$. If the minimum value is around 34 and $Q_3 = 66$, the statement "Seventy - five percent of the data values lies between 42 and 70" is incorrect.

Step4: Analyze the third statement

The whiskers of the box - plot seem to be of reasonable length, and there are no points outside the whiskers. So, it is likely that there are no outliers. The statement "It is unlikely that there are any outliers" is correct.

Step5: Calculate the inter - quartile range

The inter - quartile range $IQR=Q_3 - Q_1$. If $Q_1 = 42$ and $Q_3 = 66$, then $IQR=66 - 42=24$. The statement "The inter - quartile range is 24" is correct.

Step6: Calculate the range

The range is the difference between the maximum and minimum values. If the maximum value is around 78 and the minimum value is around 34, then the range is $78 - 34 = 44\neq36$. The statement "The range is 36" is incorrect.

Answer:

It is unlikely that there are any outliers. The inter - quartile range is 24.