Let’s analyze the box-and-whisker plots for Classes A and B to answer each question:

(a) A score above 70 is considered passing. Which class had more passing scores?

For a box plot, the range from the lower whisker to the upper whisker shows the distribution of all scores. If we assume that the number of students in each class is the same, then more scores above 70 can be determined by looking at where 70 lies in the plot.

In Class B, the minimum score (lower whisker) is below 70, but the first quartile (Q1) is slightly above 70, indicating that more than 75% of the scores are above 70.
In Class A, however, 70 is slightly below the median but within the interquartile range (IQR), suggesting that around half the scores are above 70.

Thus, Class B likely has more passing scores.

(b) Which class had test scores with a larger interquartile range (IQR)?

The IQR is the distance between the first quartile (Q1) and the third quartile (Q3), representing the middle 50% of the data.

From observation:

• Class A has a wider IQR (spanning from about 68 to 85).
• Class B has a smaller IQR (spanning from about 73 to 82).

Therefore, Class A has a larger IQR.

(c) Which class had the highest test score?

The highest test score is represented by the upper whisker endpoint in each box plot.

• Class A has an upper whisker reaching 100.
• Class B has an upper whisker reaching around 95.

So, Class A had the highest test score.

(d) Which class had a higher median test score?

The median is represented by the line inside each box.

• Class A has a median around 77.
• Class B has a median around 78.

Thus, Class B has a slightly higher median test score.

Let me know if you want further details on any part of the analysis or have any questions.

Related Questions:

1. What is the significance of a larger interquartile range in test score distributions?
2. How does the spread of scores affect the interpretation of overall class performance?
3. Why is the median an important measure of central tendency in this context?
4. How might outliers affect the interpretation of each class’s test scores?
5. In what situations might the range or IQR be more informative than the median?

Tip: When interpreting box plots, remember that the IQR (middle 50% of data) indicates data consistency – the narrower it is, the more consistent the scores around the median.