Question

the pathogen phytophthora capsici causes bell pepper plants to wilt and die. a research project was designed to study the effect of soil water content and the spread of the disease in fields of bell. it is thought that too much water helps spread the disease. the fields were divided into rows and quadrants. the soil water content (percent of water by volume of soil) was determined for each plot. an important first - step in such a research project is to give a statistical description of the data.
soil water content for bell pepper study
6 6 7 8 8 8 9 9 9 9 9 9 10
10 10 10 10 10 10 10 11 11 11 11 11 12
12 12 12 12 12 12 13 13 13 13 13 14 14
14 14 14 15 15 15 15 15 16 16 17
(a) make a box - and - whisker plot of the data.

Explanation:

Step1: Arrange data in ascending order

The data is already in ascending - order: 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 17

Step2: Find the minimum value

The minimum value is 6.

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

There are $n = 49$ data points. The position of $Q_1$ is $i=\frac{n + 1}{4}=\frac{49+1}{4}=12.5$. So, $Q_1$ is the average of the 12th and 13th ordered data values. The 12th value is 9 and the 13th value is 10, so $Q_1=\frac{9 + 10}{2}=9.5$.

Step4: Find the median ($Q_2$)

The position of the median is $i=\frac{n + 1}{2}=\frac{49+1}{2}=25$. So the median $Q_2 = 12$.

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

The position of $Q_3$ is $i=\frac{3(n + 1)}{4}=\frac{3\times(49 + 1)}{4}=37.5$. So, $Q_3$ is the average of the 37th and 38th ordered data values. The 37th value is 14 and the 38th value is 14, so $Q_3 = 14$.

Step6: Find the maximum value

The maximum value is 17.

Step7: Draw the box - and - whisker plot

Draw a number line that includes the range from 6 to 17. Draw a box from $Q_1 = 9.5$ to $Q_3 = 14$, with a vertical line inside the box at the median $Q_2 = 12$. Draw whiskers from the box to the minimum value 6 and the maximum value 17.

Answer:

To draw the box - and - whisker plot: Mark the minimum value 6, $Q_1=9.5$, median $Q_2 = 12$, $Q_3 = 14$, and maximum value 17 on a number line. Draw a box from 9.5 to 14 with a line at 12 inside the box, and whiskers from the box to 6 and 17.