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Chapter 3: Problem 21

In the most recent summer Olympics, do you think the standard deviation of the running times for all men who ran the 100 -meter race would be larger or smaller than the standard deviation of the running times for the men's marathon? Explain.

Short Answer

Expert verified
The standard deviation of the running times for the men's marathon would likely be larger than the 100-meter race due to the larger spread of running times in a marathon race.

Step by step solution

01

Understanding Standard Deviation

Standard deviation is a measure of how spread out numbers in a data set are. It's the square root of the variance. If the data points are all close to the mean, then the standard deviation is small; if the data points are spread out over a large range of values, the standard deviation is large.
02

Analyze The Features Of The Races

The 100 meter race is a sprint that lasts a few seconds. The aim of the athletes is to maintain the maximum speed over the entire course. As a result, the times obtained by the competitors are often very close to each other. \n\nIn contrast, a marathon is a long-distance race where the strategies can be very diverse depending on the runners. Some athletes may start fast, others slow, and the pace can change during the race. Not to mention external factors such as weather and physical condition can greatly affect the times. Therefore, the data spread in a marathon's running times would be expected to be larger.
03

Drawing Conclusion

Considering that a larger spread of data points leads to a larger standard deviation, it is reasonable to conclude that the standard deviation of the running times for the men's marathon would likely be larger than that of the 100-meter race.

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Most popular questions from this chapter

Construct two sets of numbers with at least five numbers in each set with the following characteristics: The means are different, but the standard deviations are the same. Report the standard deviation and both means.

The prices (in \$ thousand) of a sample of three-bedroom homes for sale in South Carolina and Tennessee are shown in the following table. Write a report that compares the prices of these homes. In your report, answer the questions of which state had the most expensive homes and which had the most variability in home prices. (Source: Zillow.com) $$ \begin{array}{|c|c|} \hline \text { South Carolina } & \text { Tennessee } \\ \hline 292 & 200 \\ \hline 323 & 205 \\ \hline 130 & 400 \\ \hline 190 & 138 \\ \hline 110 & 190 \\ \hline 183 & 292 \\ \hline 185 & 127 \\ \hline \end{array} $$ $$ \begin{array}{|c|c|} \hline \text { South Carolina } & \text { Tennessee } \\ \hline 160 & 183 \\ \hline 205 & 215 \\ \hline 165 & 280 \\ \hline 334 & 200 \\ \hline 160 & 220 \\ \hline 180 & 125 \\ \hline 134 & 160 \\ \hline 221 & 302 \\ \hline \end{array} $$

Construct two sets of numbers with at least five numbers in each set with the following characteristics: The mean of set \(A\) is smaller than that of set \(B\), but the median of set \(B\) is smaller than that of set A. Report the mean and the median of both sets of data.

The tables below show the 2015 unemployment rates for states in the northeastern and midwestern regions of the United States. Compare the unemployment rates for the two regions, commenting on the typical unemployment rate of each region and then comparing the amount of variation in the unemployment rate for each region. (Source: 2017 World Almanac and Book of Facts) Northeast States \(\begin{array}{llllllll}5.6 & 5 & 3.4 & 5.6 & 5.3 & 5.1 & 5 & 3.7\end{array}\) Midwest States \(\begin{array}{llllllllll}5.9 & 4.8 & 3.7 & 4.2 & 5.4 & 3.7 & 5 & 3 & 2.7 & 4.9\end{array}\) \(\begin{array}{ll}3.1 & 4.6\end{array}\)

The mean weight gain for women during a full-term pregnancy is \(30.2\) pounds. The standard deviation of weight gain for this group is \(9.9\) pounds, and the shape of the distribution of weight gains is symmetric and unimodal. (Source: BMJ 2016; 352 doi: https://doi.org/10.1136/bmj.i555) a. State the weight gain for women one standard deviation below the mean and for one standard deviation above the mean. b. Is a weight gain of 35 pounds more or less than one standard deviation from the mean?
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