Question

1. the students in ms. glenns math class earned the grades shown below.

65, 70, 70, 80, 80, 82, 88, 88, 90, 90, 95
which box - and - whisker plot represents these data?

Explanation:

Step1: Find the minimum value

The minimum value in the data set \(65, 70, 70, 80, 80, 82, 88, 88, 90, 90, 95\) is \(65\).

Step2: Find the first quartile (\(Q_1\))

The data set has \(n = 11\) values. The position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{11 + 1}{4}=3\)rd value. The 3rd value is \(70\), so \(Q_1 = 70\).

Step3: Find the median (\(Q_2\))

The position of the median is \(\frac{n + 1}{2}=\frac{11+ 1}{2}=6\)th value. The 6th value is \(82\), so the median \(Q_2 = 82\).

Step4: Find the third quartile (\(Q_3\))

The position of \(Q_3\) is \(\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9\)th value. The 9th value is \(90\), so \(Q_3 = 90\).

Step5: Find the maximum value

The maximum value in the data set is \(95\).

Now we analyze the box - and - whisker plots:

• The minimum value should be \(65\), so we can eliminate plots where the left whisker starts at a value other than around \(65\).
• The first quartile \(Q_1 = 70\), the median \(Q_2=82\), the third quartile \(Q_3 = 90\) and the maximum value \(= 95\).

Looking at the plots:

• Plot 1: The left whisker starts at \(65\) (matches our minimum), \(Q_1 = 70\), median \(= 82\), \(Q_3=90\) and maximum \( = 95\).
• Plot 2: The left whisker does not start at \(65\), so we eliminate it.
• Plot 3: The left whisker does not start at \(65\), so we eliminate it.
• Plot 4: The left whisker does not start at \(65\), so we eliminate it.

Answer:

1. The box - and - whisker plot with minimum \(65\), \(Q_1 = 70\), median \(82\), \(Q_3 = 90\) and maximum \(95\) (the first plot).