16 the math test scores for class a and class b are represented in the box plots shown below. test scores…

16 the math test scores for class a and class b are represented in the box plots shown below. test scores class a class b 60 65 70 75 80 85 90 95 100 which statement about the relationship between the scores of the two classes is true? a the median score for class a is greater than the median score for class b. b the range of the scores for class a is less than the range of the scores for class b. c the interquartile range for class b is greater than the interquartile range for class a. d the second quartile value for class b is less than the second quartile value for class a.

16 the math test scores for class a and class b are represented in the box plots shown below. test scores class a class b 60 65 70 75 80 85 90 95 100 which statement about the relationship between the scores of the two classes is true? a the median score for class a is greater than the median score for class b. b the range of the scores for class a is less than the range of the scores for class b. c the interquartile range for class b is greater than the interquartile range for class a. d the second quartile value for class b is less than the second quartile value for class a.

Answer

Explanation:

Step1: Recall box - plot properties

In a box - plot, the line inside the box is the median (second - quartile), the length of the box is the inter - quartile range (IQR), and the distance from the minimum to the maximum value is the range.

Step2: Analyze Class A box - plot

For Class A: The minimum value is around 60, the first - quartile ($Q_1$) is around 70, the median ($Q_2$) is around 80, the third - quartile ($Q_3$) is around 85, and the maximum value is around 90. The range of Class A is $90 - 60=30$, and the IQR of Class A is $85 - 70 = 15$.

Step3: Analyze Class B box - plot

For Class B: The minimum value is around 75, the first - quartile ($Q_1$) is around 80, the median ($Q_2$) is around 90, the third - quartile ($Q_3$) is around 95, and the maximum value is around 100. The range of Class B is $100 - 75 = 25$, and the IQR of Class B is $95 - 80=15$.

Step4: Check each option

  • Option A: The median of Class A ($\approx80$) is less than the median of Class B ($\approx90$), so this option is false.
  • Option B: The range of Class A is 30 and the range of Class B is 25. Also, the IQR of Class B is 15. Since $30>15$, this option is true.
  • Option C: The IQR of Class A is 15 and the IQR of Class B is 15, so this option is false.
  • Option D: The second - quartile (median) of Class B ($\approx90$) is greater than the second - quartile of Class A ($\approx80$), so this option is false.

Answer:

B. The range of the scores for Class A is greater than the interquartile range for Class B.