Question

test scores
ms. dobsons class
district - wide
0 10 20 30 40 50 60 70 80 90 100 110
which statement is true about the box plots? select three options.
□ ms. dobsons class has a smaller range of scores.
□ the district has a greater interquartile range.
□ fifteen is an outlier for the districts scores.
□ one hundred is an outlier for the districts scores.
□ in general, the districts scores were better than those of ms. dobsons class.

Explanation:

Step1: Analyze Range

Range is max - min. Ms. Dobson’s class box plot has a shorter whisker span (from ~45 to 95, range ~50) vs district (from ~20 to 100, range ~80). So "Ms. Dobson’s class has a smaller range" is true.

Step2: Analyze Interquartile Range (IQR)

IQR is Q3 - Q1. District’s box (between 60 - 80? Wait, no: district’s box is wider (from ~60 to 80? Wait, Ms. Dobson’s box is narrower. Wait, district’s box spans from ~60 to 80? No, looking at the plot: Ms. Dobson’s box is around 70 - 80? Wait, no, the x - axis: district - wide box starts at ~20 (whisker start) and box from ~60 to 80? Wait, no, the box plot: Ms. Dobson’s class box is more to the right, with whiskers from ~45 to 95, box from ~70 to 80. District - wide: whiskers from ~20 to 100, box from ~60 to 80. So IQR for district: 80 - 60 = 20? Ms. Dobson’s: 80 - 70 = 10? So district has greater IQR. So "The district has a greater interquartile range" is true.

Step3: Analyze Outliers

Outlier formula: Q1 - 1.5IQR and Q3 + 1.5IQR. For district: Q1 is ~60, IQR is ~20 (from above). Q1 - 1.5IQR = 60 - 30 = 30. 15 is less than 30, so 15 is an outlier? Wait, no, district’s lower whisker starts at ~20, so 15 is below Q1 - 1.5IQR (30), so 15 is an outlier. For upper: Q3 = 80, Q3 + 1.5*IQR = 80+30 = 110. 100 is less than 110, so not an outlier. Now, "Fifteen is an outlier for the district’s scores" is true. "One hundred is an outlier" is false (since 100 < 110). "In general, the district’s scores were better" is false because Ms. Dobson’s scores are more to the right (higher median, higher scores). So the three true statements are: "Ms. Dobson’s class has a smaller range of scores", "The district has a greater interquartile range", "Fifteen is an outlier for the district’s scores".

Answer:

• Ms. Dobson’s class has a smaller range of scores.
• The district has a greater interquartile range.
• Fifteen is an outlier for the district’s scores.