the pathogen phytophthora capsici causes bell pepper plants to wilt and die. a research project was designed…

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.\nsoil water content for bell pepper study\n6 6 7 8 8 8 9 9 9 9 9 9 10\n10 10 10 10 10 10 10 11 11 11 11 11 12\n12 12 12 12 12 12 13 13 13 13 13 14 14\n14 14 14 15 15 15 15 15 16 16 17\n(a) make a box - and - whisker plot of the data.

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.\nsoil water content for bell pepper study\n6 6 7 8 8 8 9 9 9 9 9 9 10\n10 10 10 10 10 10 10 11 11 11 11 11 12\n12 12 12 12 12 12 13 13 13 13 13 14 14\n14 14 14 15 15 15 15 15 16 16 17\n(a) make a box - and - whisker plot of the data.

Answer

Explanation:

Step1: Find the minimum value

The minimum value in the data - set is 6.

Step2: Find the first quartile ($Q_1$)

First, find the position of $Q_1$. The formula for the position of $Q_1$ for a data - set of size $n$ is $L_{Q_1}=\frac{n + 1}{4}$. Here, $n = 50$. So, $L_{Q_1}=\frac{50+1}{4}=12.75$. The first quartile is the value at the 12.75th position. Interpolating between the 12th and 13th ordered values. The 12th value is 10 and the 13th value is 10, so $Q_1 = 10$.

Step3: Find the median ($Q_2$)

The formula for the position of the median for a data - set of size $n$ (even) is $L_{Q_2}=\frac{n}{2}$ and $\frac{n}{2}+1$. For $n = 50$, $L_{Q_2}=\frac{50}{2}=25$ and $26$. The median is the average of the 25th and 26th ordered values. Both the 25th and 26th values are 12, so $Q_2 = 12$.

Step4: Find the third quartile ($Q_3$)

The formula for the position of $Q_3$ is $L_{Q_3}=\frac{3(n + 1)}{4}$. For $n = 50$, $L_{Q_3}=\frac{3(50 + 1)}{4}=38.25$. Interpolating between the 38th and 39th ordered values. The 38th value is 13 and the 39th value is 13, so $Q_3 = 13$.

Step5: Find the maximum value

The maximum value in the data - set is 17.

Step6: Draw the box - and - whisker plot

Draw a number line that includes the range from 6 to 17. Draw a box from $Q_1 = 10$ to $Q_3 = 13$, 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:

The box - and - whisker plot has a minimum value of 6, $Q_1 = 10$, median $Q_2 = 12$, $Q_3 = 13$, and a maximum value of 17.