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 peppers. 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
15 14 14 14 13 12 11 11 11 11 10 11 13 16 10 9
15 12 9 10 7 14 13 14 8 9 8 11 13 13 15 12 9 10
9 9 16 16 12 10 11 11 12 15 6 10 10 10 11 9

Required:
a. Make a box-and-whisker plot of the data. Find the interquartile range.
b. Grouped Data Make a frequency table using four classes. Then estimate the mean and sample standard deviation using the frequency table. Compute a 75% Chebyshev interval centered about the mean.
c. If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation.

Answer 1

Answer: 1. Order the number from smallest to largest:

6, 7,8, 8, 9,9, 9, 9, 9,9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16

Since the number of scores is even, the median is the average of the middle scores:

The first quartile is the median of the data values below the median (or at 25% of the data):

The third quartile is the median of the data values above the median (or at 75% of the data):

The interquartile range IQR is the difference of the third and first quartile:

IQR=13-10=3

2.The whiskers of the boxplot are at the minimum and maximum value. The box starts at the lower quartile, end at the upper quartile and has a vertical line at the median.

The lower quartile is at 25% of the sorted data list, the median at 50% and the upper quartile at 75%.

[Graph]

Explanation: