Question

the box plots compare the exam scores of ms. dobsons class to the rest of the students who took the test in the district. test scores ms. dobsons class district - wide 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.

Explanation:

Step1: Calculate the range

The range is the difference between the maximum and minimum values.
For Ms. Dobson's class: assume max is \(x_1\), min is \(y_1\), range \(R_1=x_1 - y_1\). From the box - plot, Ms. Dobson's class has a smaller spread (max - min) compared to the district.

Step2: Calculate the inter - quartile range (IQR)

The IQR is \(Q_3 - Q_1\). For the district, the box (representing IQR) is wider than that of Ms. Dobson's class.

Step3: Check for outliers

Outliers are values that are less than \(Q_1-1.5\times IQR\) or greater than \(Q_3 + 1.5\times IQR\).
For the district's scores, 15 is not an outlier (as per the box - plot spread and typical outlier calculation range which is much lower than 15 for this data spread). 100 is also not an outlier (the upper whisker and box spread do not indicate 100 as an extreme value beyond \(Q_3+1.5\times IQR\) for this data).

Answer:

Ms. Dobson's class has a smaller range of scores. The district has a greater interquartile range.