Analyze Data Shape and Context Quick Check
5 of 55 of 5 Items
Question
Use the image to answer the 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 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.
The range of the science scores is higher than the range 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 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.
To analyze the given datasets using the box plots, we can determine the following:
1. The first statement is true. The math scores have a smaller spread than the science scores. This can be observed by comparing the distance between the minimum and maximum values in each box plot. The difference between the minimum and maximum values is smaller for the math scores than for the science scores.
2. The second statement is false. The range of the math scores is 25 - 5 = 20. The range of the science scores is 24 - 6 = 18. Therefore, the range of the math scores is higher than the range of the science scores.
3. The third statement is false. The median of the math scores is 15 and the median of the science scores is 16. Therefore, the median of the science scores is higher than the median of the math scores.
4. The fourth statement is true. The interquartile range (IQR) is the difference between the third quartile and the first quartile. For the math scores, the IQR is 20 - 10 = 10. For the science scores, the IQR is 20 - 12 = 8. Therefore, the IQR of the science scores is lower than the IQR of the math scores.
So, the answer is: The interquartile range (IQR) of the science scores is lower than the IQR of the math scores.