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Chapter 3: Problem 74

Briefly explain what summary measures are used to construct a box-and-whisker plot.

Short Answer

Expert verified
The summary measures used to construct a box-and-whisker plot are the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. The box represents the IQR (Q1 to Q3), with the line in the box indicating the median. The whiskers extend to the minimum and maximum values of the data, excluding outliers, which are indicated separately.

Step by step solution

01

Understanding the Components

A box-and-whisker plot is composed of a box and two whiskers. The box represents the interquartile range (IQR), which is the range between the first quartile (Q1, the 25th percentile) and the third quartile (Q3, the 75th percentile). The line within the box represents the median (Q2, the 50th percentile) of the data set.
02

Understanding the Whiskers

The whiskers on the plot represent the variability outside the IQR. One whisker extends from Q1 to the smallest non-outlier (also simply referred to as the minimum) in the data set, whereas the other extends from Q3 to the largest non-outlier (also called the maximum value) in the data set.
03

Identification of Outliers

Any data points that are outside the whiskers are considered outliers. These are points that are significantly smaller or larger than the rest of the data.

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Most popular questions from this chapter

For any data, the sum of all values is equal to the product of the sample size and mean; that is, \(\Sigma x=n \bar{x}\). Suppose the average amount of money spent on shopping by 10 persons during a given week is \(\$ 105.50 .\) Find the total amount of money spent on shopping by these 10 persons.

The mean 2015 income for five families was \(\$ 99,520\). What was the total 2015 income of these five families?

The following data give the 2015 bonuses (in thousands of dollars) of 10 randomly selected Wall Street managers. \(\begin{array}{llllllllll}127 & 82 & 45 & 99 & 153 & 3261 & 77 & 108 & 68 & 278\end{array}\) a. Calculate the mean and median for these data. b. Do these data have a mode? Explain why or why not. c. Calculate the \(10 \%\) trimmed mean for these data. d. This data set has one outlier. Which summary measures are better for these data?

The following data give the number of driving citations received during the last three years by 12 drivers. \(\begin{array}{llllllllllll}4 & 8 & 0 & 3 & 11 & 7 & 4 & 14 & 8 & 13 & 7 & 9\end{array}\) a. Find the mean, median, and mode for these data. b. Calculate the range, variance, and standard deviation. c. Are the values of the summary measures in parts a and \(\mathrm{b}\) population parameters or sample statistics?

The mean time taken by all participants to run a road race was found to be 220 minutes with a standard deviation of 20 minutes. Using Chebyshev's theorem, find the minimum percentage of runners who completed the race in a. 180 to 260 minutes b. 160 to 280 minutes c. 170 to 270 minutes
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