3. Describing Data Numerically

"The Empirical Rule SAT Math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114.

Source: College Board

a. What percentage of SAT scores is between 401 and 629?"

The Empirical Rule SAT Math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114.

Source: College Board

b. What percentage of SAT scores is less than 401 or greater than 629?

The Empirical Rule SAT Math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114.

Source: College Board

c. What percentage of SAT scores is greater than 743?

Identical Values Compute the sample standard deviation of the following test scores: 78, 78, 78, 78. What can be said about a data set in which all the values are identical?

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.

Explain how the standard deviation measures dispersion. In your explanation, include a discussion of deviation about the mean.

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.

b. Explain why the mean is higher for Camaros yet the standard deviation is less.

Sullivan Survey Choose any quantitative variable from the SullivanStatsSurveyI at www.pearsonhighered.com/sollivanstats. Now choose a qualitative variable, such as gender or political philosophy. Determine the range and standard deviation by the qualitative variable chosen. For example, if you chose gender as the qualitative variable, determine the range and standard deviation by gender. Does there appear to be any difference in the measure of dispersion for each level of the qualitative variable?

What is meant by the phrase degrees of freedom as it pertains to the computation of the sample standard deviation?

What makes the range less desirable than the standard deviation as a measure of dispersion?

In one of Sollivan’s statistics sections, the standard deviation of the heights of all students was 3.9 inches. The standard deviation of the heights of males was 3.4 inches and the standard deviation of females was 3.3 inches. Why is the standard deviation of the entire class more than the standard deviation of the males and females considered separately?

The ________ represents the number of standard deviations an observation is from the mean.

The following data represent the length of time (in minutes) between eruptions of Old Faithful in Yellowstone National Park.

b. Approximate the standard deviation length of time between eruptions.

"[DATA] Putting It Together: Paternal Smoking It is well-documented that active maternal smoking during pregnancy is associated with lower-birth-weight babies. Researchers wanted to determine if there is a relationship between paternal smoking habits and birth weight. The researchers administered a questionnaire to each parent of newborn infants. One question asked whether the individual smoked regularly. Because the survey was administered within 15 days of birth, it was assumed that any regular smokers were also regular smokers during pregnancy. Birth weights for the babies (in grams) of nonsmoking mothers were obtained and divided into two groups, nonsmoking fathers and smoking fathers. The given data are representative of the data collected by the researchers. The researchers concluded that the birth weight of babies whose father smoked was less than the birth weight of babies whose father did not smoke.

e. Determine summary statistics (mean, median, standard deviation, quartiles) for each group."

Exit Velocity Use the frequency distribution whose class width is 4 obtained in Problem 25 in Section 2.2 to approximate the mean and standard deviation exit velocity. Compare these results to the actual mean and standard deviation exit velocity.