Question

here are the scores of 15 students on an algebra test. 56, 59, 68, 68, 72, 73, 74, 75, 76, 80, 80, 82, 84, 86, 90. notice that the scores are ordered from least to greatest. make a box - and - whisker plot for the data.

Explanation:

Step1: Find the minimum value

The minimum value of the data - set 56, 59, 68, 68, 72, 73, 74, 75, 76, 80, 80, 82, 84, 86, 90 is 56.

Step2: Find the first quartile ($Q_1$)

The data - set has $n = 15$ values. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{15+1}{4}=4$. So, $Q_1$ is the 4th value in the ordered data - set, which is 68.

Step3: Find the median ($Q_2$)

The position of the median is $\frac{n + 1}{2}=\frac{15 + 1}{2}=8$. So, the median $Q_2$ is the 8th value in the ordered data - set, which is 75.

Step4: Find the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(15 + 1)}{4}=12$. So, $Q_3$ is the 12th value in the ordered data - set, which is 82.

Step5: Find the maximum value

The maximum value of the data - set is 90.

To draw the box - and - whisker plot:

• Draw a number line that includes the range from 55 to 90.
• Mark a point at the minimum value (56), $Q_1$ (68), the median (75), $Q_3$ (82), and the maximum value (90).
• Draw a box from $Q_1$ to $Q_3$ with a vertical line inside the box at the median.
• Draw whiskers from the box to the minimum and maximum values.

Answer:

The box - and - whisker plot has a minimum value of 56, $Q_1 = 68$, median = 75, $Q_3 = 82$, and a maximum value of 90.