Question

1. the following grades were earned by students in ms. glenn’s math class: 65, 70, 70, 80, 80, 82, 88, 88, 90, 90, 95 construct a box plot for these grades and describe the distribution.

Explanation:

Step1: Arrange data in ascending order

65, 70, 70, 80, 80, 82, 88, 88, 90, 90, 95

Step2: Find the minimum value

The minimum value is 65.

Step3: Find the first - quartile ($Q_1$)

There are $n = 11$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{11+ 1}{4}=3$. So $Q_1 = 70$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n + 1}{2}=\frac{11+1}{2}=6$. So $Q_2=82$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9$. So $Q_3 = 90$.

Step6: Find the maximum value

The maximum value is 95.

Step7: Construct the box - plot

Draw a number line that includes the range from 65 to 95. Draw a box from $Q_1 = 70$ to $Q_3=90$ with a vertical line at the median $Q_2 = 82$. Draw whiskers from the box to the minimum (65) and maximum (95) values.

Step8: Describe the distribution

The distribution is slightly right - skewed since the distance from the median to the third - quartile ($90 - 82=8$) is larger than the distance from the median to the first - quartile ($82 - 70 = 12$), and the right - hand whisker is longer than the left - hand whisker.

Answer:

Box - plot: A box from 70 to 90 with a line at 82, whiskers to 65 and 95. Distribution: Slightly right - skewed.