The box plots below represent the scores for games played by two high school basketball teams over the last 5 seasons.

Question

A double box plot has scores from 40 to 96. The box plot labeled Central high school, has the end of first whisker at 48, the box starts at 52, the line inside the box is at halfway between 56 and 60, the box ends at 68, and the end of the second whisker is at 84. The second box plot labeled South County high school, has the end of first whisker at 44, the box starts at 52, the line inside the box is at 56, the box ends at 68, and the end of the second whisker is at 72.

Based on these plots, which statement regarding the means of the two data sets is is most likely true?

A.
The mean score per game is higher for Central High School than for South County High School because the distribution of Central High School's scores is skewed right and contains large outliers.

B.
The mean score per game is higher for South County High School because the distribution of South County High School's scores is not as skewed as the distribution of Central High School's scores.

C.
The mean score per game is about the same for both schools because their median scores are about the same.

D.
No conclusion can be drawn regarding the means because the box plots only show medians and quartiles.

Answer 1

To analyze the statement options based on the given box plots for Central High School and South County High School, let's summarize the information provided:

• Central High School:

  • Whisker (lower) = 48
  • Lower Quartile (Q1) = 52
  • Median (Q2) = between 56 and 60 (roughly 58)
  • Upper Quartile (Q3) = 68
  • Whisker (upper) = 84

• South County High School:

  • Whisker (lower) = 44
  • Lower Quartile (Q1) = 52
  • Median (Q2) = 56
  • Upper Quartile (Q3) = 68
  • Whisker (upper) = 72

Now we can analyze the options provided:

A. The mean score per game is higher for Central High School than for South County High School because the distribution of Central High School's scores is skewed right and contains large outliers.

• This statement makes a specific assertion about skewness and outliers, which can affect the mean. However, while Central has a higher upper whisker, the median isn’t necessarily indicative of a larger mean without more data.

B. The mean score per game is higher for South County High School because the distribution of South County High School's scores is not as skewed as the distribution of Central High School's scores.

• This option assumes that South County's distribution is less skewed based on the visual box plot, suggesting a higher mean. Again, without explicit data on how the scores are distributed, we cannot definitively state this about the means.

C. The mean score per game is about the same for both schools because their median scores are about the same.

• While both schools have similar median values, the mean can differ significantly from the median, particularly with different distributions.

D. No conclusion can be drawn regarding the means because the box plots only show medians and quartiles.

• This option reflects the reality that box plots mainly provide information about the spread, median, and potential outliers but do not display the actual means directly.

Considering this analysis, the most accurate statement based on the limitations of what box plots represent is:

D. No conclusion can be drawn regarding the means because the box plots only show medians and quartiles.