Question

(a) Make a box-and-whisker plot of the data. Find the interquartile range.

Study design
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asked 2021-08-14

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
\(\begin{array}{cc} 15&14&14&14&3&12&11&11&11&11&10&11&13&16&10\\ 9&15&12&9&10&7&14&13&14&8&9&8&11&13&13 \\ 15&12&9&10&9&9&16&16&12&10&11&11&12&15&8\\ 10&10&10&11&9 \end{array}\)
(a) Make a box-and-whisker plot of the data. Find the interquartile range.

Answers (1)

2021-08-15
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:
\(\displaystyle{M}={Q}_{{{2}}}={\frac{{{11}+{11}}}{{{2}}}}={11}\)
The first quartile is the median of the data values below the median (or at 25% of the data):
\(\displaystyle{Q}_{{{1}}}={10}\)
The third quartile is the median of the data values above the median (or at 75% of the data):
\(\displaystyle{Q}_{{{3}}}={13}\)
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]
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