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: Recall range formula

Range = Maximum - Minimum
For Ms. Dobson's class, maximum is around 95 and minimum is around 50, so range is $95 - 50=45$. For district - wide, maximum is around 110 and minimum is around 20, so range is $110 - 20 = 90$. So Ms. Dobson's class has a smaller range.

Step2: Recall inter - quartile range (IQR) formula

IQR = $Q_3-Q_1$. For Ms. Dobson's class, $Q_1\approx65$, $Q_3\approx85$, so $IQR_{class}=85 - 65 = 20$. For district - wide, $Q_1\approx60$, $Q_3\approx80$, so $IQR_{district}=80 - 60=20$. They have the same IQR.

Step3: Recall outlier rule

Outliers are values less than $Q_1 - 1.5\times IQR$ or greater than $Q_3+1.5\times IQR$. For district - wide, $Q_1 = 60$, $Q_3 = 80$, $IQR = 20$. $Q_1-1.5\times IQR=60-1.5\times20=60 - 30 = 30$, $Q_3 + 1.5\times IQR=80+1.5\times20=80 + 30=110$. Since $15<30$, 15 is an outlier for the district's scores. And 100 is not an outlier as $100<110$.

Answer:

Ms. Dobson's class has a smaller range of scores.
The district has a greater interquartile range. (False, they are equal)
Fifteen is an outlier for the district's scores.
One hundred is an outlier for the district's scores. (False)
So the correct options are:
Ms. Dobson's class has a smaller range of scores.
Fifteen is an outlier for the district's scores.