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 50 and 110.\nseventy - five percent of the data values lies between 20 and 50.\nit is unlikely that there are any outliers.\nthe interquartile range is 25.\nthe range is 78.

which statements about the box plot are correct? check all that apply.\nfifty percent of the data values lies between 50 and 110.\nseventy - five percent of the data values lies between 20 and 50.\nit is unlikely that there are any outliers.\nthe interquartile range is 25.\nthe range is 78.

Answer

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. The whiskers extend to the non - outlier data points.

Step2: Analyze the first statement

The box in the box - plot has left - hand side at approximately 25 and right - hand side at approximately 50. The inter - quartile range (IQR) is $Q_3 - Q_1$. Here, $Q_1\approx25$ and $Q_3\approx50$, so 50% of the data lies between 25 and 50, not 50 and 110. So the first statement is incorrect.

Step3: Analyze the second statement

75% of the data lies below $Q_3$. Here, $Q_3\approx50$ and the minimum value (assuming no outliers) is around 20. But 75% of the data lies below $Q_3 = 50$, not between 20 and 50 in the sense of "75% of the data values lies between". So the second statement is incorrect.

Step4: Analyze the third statement

The whiskers seem to be of reasonable length. Since the whiskers do not extend extremely far from the box, it is unlikely that there are any outliers. This statement is correct.

Step5: Analyze the fourth statement

The inter - quartile range $IQR=Q_3 - Q_1$. From the box - plot, $Q_1\approx25$ and $Q_3\approx50$, so $IQR = 50 - 25=25$. This statement is correct.

Step6: Analyze the fifth statement

The range is the difference between the maximum and minimum values. The maximum value is approximately 125 and the minimum value is approximately 20. So the range is $125 - 20 = 105$, not 78. This statement is incorrect.

Answer:

It is unlikely that there are any outliers; The interquartile range is 25.