Question

here are yesterdays high temperatures (in fahrenheit) in 18 u.s. cities. 50, 51, 56, 58, 59, 61, 64, 65, 66, 68, 70, 72, 72, 74, 75, 76, 77, 84. notice that the temperatures 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 is 50.

Step2: Find the first quartile ($Q_1$)

There are $n = 18$ data points. The position of $Q_1$ is at $\frac{n + 1}{4}=\frac{18+1}{4}=4.75$. So, $Q_1=58+(59 - 58)\times0.75 = 58.75$.

Step3: Find the median ($Q_2$)

The position of the median is at $\frac{n+1}{2}=\frac{18 + 1}{2}=9.5$. So, $Q_2=\frac{66+68}{2}=67$.

Step4: Find the third quartile ($Q_3$)

The position of $Q_3$ is at $\frac{3(n + 1)}{4}=\frac{3\times(18+1)}{4}=14.25$. So, $Q_3=74+(75 - 74)\times0.25 = 74.25$.

Step5: Find the maximum value

The maximum value of the data - set is 84.

Answer:

On the box - and - whisker plot:

• The left - most point (minimum) is at 50.
• The left edge of the box (first quartile) is at 58.75.
• The line inside the box (median) is at 67.
• The right edge of the box (third quartile) is at 74.25.
• The right - most point (maximum) is at 84.