Question

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. in general, the districts scores were better than those of ms. dobsons class.

Explanation:

Step1: Recall range formula

Range = Maximum - Minimum
For Ms. Dobson's class, assume minimum is around 40 and maximum is around 90, so range is \(90 - 40=50\). For district - wide, assume minimum is around 20 and maximum is around 100, so range is \(100 - 20 = 80\). So Ms. Dobson's class has a smaller range of scores.

Step2: Recall inter - quartile range (IQR) formula

IQR = \(Q_3-Q_1\). From the box - plot, for district - wide, \(Q_1\) is around 50 and \(Q_3\) is around 80, so \(IQR_{district}=80 - 50 = 30\). For Ms. Dobson's class, \(Q_1\) is around 60 and \(Q_3\) is around 80, so \(IQR_{class}=80 - 60=20\). The district has a greater inter - quartile range.

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, \(Q_1\approx50\), \(Q_3\approx80\), \(IQR = 30\). \(Q_1-1.5\times IQR=50-1.5\times30=50 - 45 = 5\), \(Q_3+1.5\times IQR=80 + 1.5\times30=80+45 = 125\). Since \(15>5\), 15 is not an outlier. \(100<125\), 100 is not an outlier. Also, from the box - plot, the district - wide scores are generally higher than Ms. Dobson's class scores.

Answer:

Ms. Dobson's class has a smaller range of scores.
The district has a greater interquartile range.
In general, the district's scores were better than those of Ms. Dobson's class.