Question

3 the data set represents the number of minutes ben walked each day for twelve day 25, 68, 10, 27, 80, 42, 36, 20, 26, 38, 42, 26 ben created a boxplot to display this data. choose which components of the boxplot, if any, that ben got wrong. a median b upper quartile c all are correct d lower extreme e lower quartile f upper extreme

Explanation:

Step1: Sort the data

Sort the data set \(25, 68, 10, 27, 80, 42, 36, 20, 26, 38, 42, 26\) in ascending order: \(10, 20, 25, 26, 26, 27, 36, 38, 42, 42, 68, 80\)

Step2: Find the lower extreme

The lower extreme (minimum value) is \(10\). In the box - plot, the left - most end of the whisker should be at \(10\). If it is not, the lower extreme is wrong.

Step3: Find the lower quartile

Since \(n = 12\) (even), the lower half of the data is \(10, 20, 25, 26, 26, 27\). The lower quartile \(Q_1=\frac{25 + 26}{2}=25.5\)

Step4: Find the median

The median (second quartile \(Q_2\)) for \(n = 12\) (even) is \(\frac{27+36}{2}=31.5\)

Step5: Find the upper quartile

The upper half of the data is \(36, 38, 42, 42, 68, 80\). The upper quartile \(Q_3=\frac{42 + 42}{2}=42\)

Step6: Find the upper extreme

The upper extreme (maximum value) is \(80\)

Answer:

A. Median, B. Upper Quartile, E. Lower Quartile