BackTravel Time to Work The frequency distribution listed in the table represents the travel time to work (in minutes) for a random sample of 895 U.S. adults.
b. Approximate the standard deviation travel time to work for U.S. adults.
For each of the following data sets, decide which has the higher standard deviation (set 1 or set 2), if any, without doing any computation. Explain the rationale behind your choice. Then, verify your choice by computing the standard deviation by hand.
pH in Water The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic, while a pH greater than 7 is alkaline. The following data represent the pH in samples of bottled water and tap water. a. Which type of water has more dispersion in pH using the range as the measure of dispersion?
pH in Water The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic, while a pH greater than 7 is alkaline. The following data represent the pH in samples of bottled water and tap water. b. Which type of water has more dispersion in pH using the standard deviation as the measure of dispersion?
"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?