3. Describing Data Numerically

Given the sample data set: $2$, what is the standard deviation of this sample?

z Scores. In Exercises 5–8, express all z scores with two decimal places.

Diastolic Blood Pressure of Females For the diastolic blood pressure measurements of females listed in Data Set 1 “Body Data” in Appendix B, the highest measurement is 98 mm Hg. The 147 diastolic blood pressure measurements of females have a mean of 70.2 mm Hg and a standard deviation of 11.2 mm Hg.

b. How many standard deviations is that [the difference found in part (a)]?

If the standard deviation for a sample is $s=9$, what is the variance of the sample?

A sample of $n=15$ scores has a mean of $m=20$ and a sample variance of $s^2=9$. What is the sample standard deviation?

Which of the following is the most common measure of total risk in statistics? i. $\mathrm{variance}$ ii. $\mathrm{standard\; deviation}$ iii. $\sqrt{\mathrm{variance}}$

Buying a Car The following data represent the asking price, in dollars, for a random sample of 2014 coupes (a two-door car) and a random sample of 2014 Chevy Camaros.

a. Find the mean and standard deviation price for each sample.

Estimating Standard Deviation with the Range Rule of Thumb. In Exercises 29–32, refer to the data in the indicated exercise. After finding the range of the data, use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the standard deviation computed using all of the data.

Body Temperatures Refer to Data Set 5 “Body Temperatures” in Appendix B and use the body temperatures for 12:00 AM on day 2.

ERA Champions In 2018, Jacob deGrom of the New York Mets had the lowest earned-run average (ERA is the mean number of runs yielded per nine innings pitched) of any starting pitcher in the National League, with an ERA of 1.70. Also in 2018, Blake Snell of the Tampa Bay Rays had the lowest ERA of any starting pitcher in the American League with an ERA of 1.89. In the National League, the mean ERA in 2018 was 3.611 and the standard deviation was 0.772. In the American League, the mean ERA in 2018 was 3.744 and the standard deviation was 0.893. Which player had the better year relative to his peers? Why?

Which of the following best describes the relationship between the $standarddeviation$ and the $precision$ of a procedure?

In Exercises 21–28, use the same list of cell phone radiation levels given for Exercises 17–20. Find the indicated percentile or quartile.

P30

In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.

Super Bowl Jersey Numbers Listed below are the jersey numbers of the 11 offensive players on the starting roster of the New England Patriots when they won Super Bowl LIII. What do the results tell us?

12 26 46 15 11 87 77 62 60 69 61

Given the data set $2$, $4$, $4$, $4$, $5$, $5$, $7$, $9$, what is the variance and what is the standard deviation, rounded to the nearest whole number?

Constructing a Confidence Interval In Exercises 25–28, use the data set to (b) find the sample standard deviation. Assume the population is normally distributed.

SAT Scores The SAT scores of 12 randomly selected high school seniors