Question

The box plots compare the exam scores of Ms. Dobson’s class to the rest of the students who took the test in the district. A number line goes from 0 to 110. Mrs. Dobson's class's whiskers range from 40 to 95, and the box ranges from 70 to 80. A line divides the box at 75. District-wide's whiskers range from 15 to 100, and the box ranges from 55 to 75. A line divides the box at 65. Which statement is true about the box plots? Select three options. 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. One hundred is an outlier for the district’s scores. In general, the district’s scores were better than those of Ms. Dobson’s class.

Answer 1

A,B,C

Explanation:

Answer 2

• 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.

Explanation:

Ms. Dobson’s class has a smaller range of scores.

Mrs. Dobson's class's whiskers range from 40 to 95 which means that the highest score in her class is 95 and the lowest is 40 which means her class's range is; 95 - 40 = 55.

The Districts range is; 100 - 15 = 85

The district has a greater interquartile range.

The box represents the interquartile range with the lower figure being Q₁ and the higher figure being Q₃. The line dividing the box is the Median.

District Interquartile range = 75 -55 = 20

Ms. Dobson's class interquartile range = 80 - 70 = 10

Fifteen is an outlier for the district’s scores.

In calculating outliers, the following formula is used;

For outliers below the minimum, any figure below the following formula is an outlier:

= Q1 - 1.5 * Interquartile range

District outlier = 55 - (1.5 * 20)

= 25

15 is less than 25 and so is an outlier.