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Question

Two box plots. One is labeled 'Math Scores' while the other is labeled 'Science Scores.' The plots are placed over a number line that ranges from 0 to 30 in increments of 5. The 5 number labels typical to box plots are available for both. The box plot for math scores shows the following labels: minimum: 5; first quartile: 10; median: 15; third quartile: 20; maximum: 25. The box plot for science scores shows the following labels: minimum: 6; first quartile: 12; median: 16; third quartile: 20; maximum: 24.

Which statement is true about the given datasets?

(1 point)
Responses

The interquartile range (IQR) of the science scores is lower than the IQR of the math scores.
The interquartile range (IQR) of the science scores is lower than the IQR of the math scores.

The median of the math scores is higher than the median of the science scores.
The median of the math scores is higher than the median of the science scores.

The math scores are less spread out than the science scores.
The math scores are less spread out than the science scores.

The range of the science scores is higher than the range of the math scores.

Answer 1

To analyze the box plots' data, we can calculate the necessary statistics.

1. Interquartile Range (IQR):

   • IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
   • For Math Scores:
     • Q1 = 10, Q3 = 20
     • IQR (Math) = Q3 - Q1 = 20 - 10 = 10
   • For Science Scores:
     • Q1 = 12, Q3 = 20
     • IQR (Science) = Q3 - Q1 = 20 - 12 = 8

   Comparison: IQR of Science (8) is lower than IQR of Math (10).

2. Median:

   • For Math Scores, the median is 15.
   • For Science Scores, the median is 16.

   Comparison: The median of Math (15) is lower than the median of Science (16).

3. Spread:

   • Spread can be measured using the range or IQR.
   • Range is calculated as the maximum minus the minimum.
   • For Math Scores:
     • Range = Maximum - Minimum = 25 - 5 = 20
   • For Science Scores:
     • Range = Maximum - Minimum = 24 - 6 = 18

   Comparison: The range of Science (18) is lower than the range of Math (20), meaning math scores are more spread out.

4. Statement Evaluation:

   • The interquartile range (IQR) of the science scores is lower than the IQR of the math scores. (True)
   • The median of the math scores is higher than the median of the science scores. (False)
   • The math scores are less spread out than the science scores. (False)
   • The range of the science scores is higher than the range of the math scores. (False)

Based on the analysis, the statement that is true is:

The interquartile range (IQR) of the science scores is lower than the IQR of the math scores.