Question

1. below is a list of annual precipitation in inches. create a box plot to represent the data. 27.8, 40.6, 23.6, 5, 24.6, 18.2, 8.4, 41.2, 56.6, 56.6, 42.4, 63.4, 12.8, 42.8, 5.6, 27.2

Explanation:

Step1: Order the data

$5, 5.6, 8.4, 12.8, 18.2, 23.6, 24.6, 27.2, 27.8, 40.6, 41.2, 42.4, 42.8, 56.6, 56.6, 63.4$

Step2: Find the median (Q2)

There are 16 data - points. The median is the average of the 8th and 9th ordered values. $\text{Q2}=\frac{27.2 + 27.8}{2}=27.5$

Step3: Find the lower half of data

The lower half is $5, 5.6, 8.4, 12.8, 18.2, 23.6, 24.6, 27.2$. The median of the lower half (Q1) is the average of the 4th and 5th ordered values. $\text{Q1}=\frac{12.8+18.2}{2}=15.5$

Step4: Find the upper half of data

The upper half is $27.8, 40.6, 41.2, 42.4, 42.8, 56.6, 56.6, 63.4$. The median of the upper half (Q3) is the average of the 4th and 5th ordered values. $\text{Q3}=\frac{42.4 + 42.8}{2}=42.6$

Step5: Identify the minimum and maximum

The minimum value is $5$ and the maximum value is $63.4$

Step6: Draw the box - plot

On a number - line, mark the minimum ($5$), Q1 ($15.5$), Q2 ($27.5$), Q3 ($42.6$), and maximum ($63.4$). Draw a box from Q1 to Q3 with a line inside at Q2. Draw whiskers from the box to the minimum and maximum values.

Answer:

A box - plot is drawn with minimum = 5, Q1 = 15.5, Q2 = 27.5, Q3 = 42.6, and maximum = 63.4.