Statistics salkind 4e test bank ch03

Chapter 3: Vive la Différence: Understanding Variability Test Bank MULTIPLE CHOICE Which of the following measures how scores differ from each other? a Skewness b Kurtosis c Average d Variability ANS: D PTS: DIF: Easy REF: Why Understanding Variability Is Important OBJ: Why variability is valuable as a descriptive tool COG: Knowledge Which of the following is NOT a measure of variability? a Mean b Standard deviation c Variance d Range ANS: A PTS: DIF: Easy REF: Why Understanding Variability Is Important OBJ: Why variability is valuable as a descriptive tool COG: Knowledge In order to calculate the variance, which of the following must you know? a Range b Median c Mean d Mode ANS: C PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Knowledge What is another term for variability? a Flux or variation b Scattergram c Skewness d Spread or dispersion ANS: D PTS: DIF: Easy REF: Why Understanding Variability Is Important OBJ: Why variability is valuable as a descriptive tool What are the three tools used to assess variability? a Range, standard deviation, and variance b Mean, median, and mode c Variance, range, and mean d Mean, standard deviation, and skewness ANS: A PTS: DIF: Easy REF: Why Understanding Variability Is Important COG: Knowledge OBJ: Why variability is valuable as a descriptive tool COG: Knowledge Which measure of variability is easiest to calculate? a Standard deviation b Mode c Range d Variance ANS: C PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Comprehension Which measure of variability is most general and, hence, least useful? a Median b Range c Standard deviation d Mean deviation ANS: B PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Knowledge Which measure of variability should never be used alone to reach conclusions regarding the variance of a distribution? a Standard deviation b Mode c Variance d Range ANS: D PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Knowledge Which measure of variability is a measure of the average distance from the mean? a Standard deviation b Range c Median d Mode ANS: A PTS: DIF: Easy REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance COG: Knowledge 10 What is the range for the following set of scores: 29, 48, 22, 37, 55? a 26 b 33 c 37 d 55 ANS: B PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Application 11 What is the range for the following set of scores: 34, 14, 17, 57, 22? a 14 b 17 c 57 d 43 ANS: D PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Application 12 What is the range for the following set of scores: 117, 249, 326, 47, 442? a 117 b 395 c 326 d 442 ANS: B PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Application 13 If you have a lowest score of 21 and a range of 47, your highest score will be _ a 26 b 21 c 47 d 68 ANS: D PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Application 14 Which of the following measures how different scores are from one particular score? a Average b Correlation c Variability d Standard Deviation ANS: C PTS: DIF: Easy REF: Why Understanding Variability Is Important OBJ: Why variability is valuable as a descriptive tool COG: Knowledge 15 What is the most common measure of variability? a Range b Standard deviation c Variance d Mean deviation ANS: B PTS: DIF: Easy REF: Computing the Standard Deviation OBJ: Why variability is valuable as a descriptive tool COG: Knowledge 16 When reporting descriptive data such as the mean, what additional information should also be reported that expresses how different the scores are in the distribution? a Variability b Outlier c Skew d Percentile ANS: A PTS: DIF: Easy REF: Why Understanding Variability Is Important OBJ: Why variability is valuable as a descriptive tool COG: Comprehension 17 If you subtract the smallest number in the distribution from the largest, what type of variability is being calculated? a Variance b Range c Outliers d Standard Deviation ANS: B PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Comprehension 18 In the formula for computing the range, what does the letter h represent? a Summation b Sample size c Highest score d Lowest score ANS: C PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Knowledge 19 In the formula for computing the range, what does the letter l represent? a Range b Variability c Highest score d Lowest score ANS: D PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Knowledge 20 In the formula for computing the range, this is used to represent the range: a rho b Ran c r d rhi ANS: C PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Knowledge 21 The highest score minus the lowest score is equal to the _ a Standard deviation b Inclusive range c Exclusive range d Variance ANS: C PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Knowledge 22 The highest score minus the lowest score plus one is equal to the _ a Exclusive range b Variance c Inclusive range d Standard deviation ANS: C PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Knowledge 23 In the formula for calculating the standard deviation, what does the Greek letter  represent? a Summation b Sample size c Mean score for group d Individual scores ANS: A PTS: DIF: Medium REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance COG: Knowledge 24 In the formula for calculating the variance, what does the letter n represent? a Summation b Sample size c Mean score for group d Individual score ANS: B PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Knowledge 25 When calculating the standard deviation, what must be done in order to obtain an unbiased estimate? a Subtract from X b Add to X c Subtract from n d Add to n ANS: C PTS: DIF: Medium REF: Why n – 1? What’s Wrong With Just n? OBJ: Computing the range, standard deviation, and variance COG: Knowledge 26 Which of the following sets of scores has the greatest variability? a 7, 10, 11, 15, 19 b 7, 7, 8, 8, 10, 11 c 7, 7, 7, 7, 7, d 6, 6, 7, 7, 7, ANS: A PTS: DIF: Hard REF: Why Understanding Variability Is Important OBJ: Computing the range, standard deviation, and variance COG: Application 27 Which of the following sets of scores has the least variability? a 5, 4, 5, 6, b 7, 2, 8, 9, c 12, 14, 17, 19, 21 d 1, 2, 1, 7, ANS: A PTS: DIF: Hard REF: Why Understanding Variability Is Important OBJ: Computing the range, standard deviation, and variance COG: Application 28 Variability is a measure of how much individual scores differ from the _ a Mean b Range c Standard deviation d Variance ANS: A PTS: DIF: Easy REF: Why Understanding Variability Is Important OBJ: Computing the range, standard deviation, and variance COG: Knowledge 29 What is the formula for calculating the exclusive range? a r - n + b h - l + c (h - 1) r d h - l ANS: D PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Knowledge 30 What is the formula for calculating the inclusive range? a r - n + b h - l + c (h - l) r d h - l ANS: B PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Knowledge 31 The sum of the absolute value of the deviations from the mean divided by the number of scores is equal to the _ a Mean b Standard deviation c Mean deviation d Variance ANS: C PTS: DIF: Medium REF: And Now Using Excel’s STDEV.S Function OBJ: Computing the range, standard deviation, and variance COG: Knowledge 32 The sum of the deviations from the mean will always be equal to _ a b c n - d n + ANS: A PTS: DIF: Hard REF: And Now Using Excel’s STDEV.S Function OBJ: Computing the range, standard deviation, and variance 33 What is obtained by squaring the standard deviation? a Mean deviation b Range c Variance COG: Knowledge d Squared deviation ANS: C PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Knowledge 34 What is obtained by taking the square ROOT of the variance? a Standard deviation b Mean c Mode d Mean deviation ANS: A PTS: DIF: Hard OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Comprehension 35 Which of the following is one way to represent the standard deviation? a s b s2 c s(2) d s / n ANS: A PTS: DIF: Medium REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance COG: Knowledge 36 Which of the following is one way to represent the variance? a s b s2 c s(2) d s / n ANS: B PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Knowledge 37 Unbiased estimates a Subtract from the sample size b Add to the sample size c Do not change the sample size d Multiply the sample size by ANS: A PTS: DIF: Medium REF: Why n – 1? What’s Wrong With Just n? OBJ: Computing the range, standard deviation, and variance COG: Knowledge 38 Unbiased estimates a Are less conservative estimates of sample statistics b Are more conservative estimates of sample statistics c Are less conservative estimates of population parameters d Are more conservative estimates of population parameters ANS: D PTS: DIF: Medium REF: Why n – 1? What’s Wrong With Just n? OBJ: Computing the range, standard deviation, and variance COG: Knowledge 39 What is the range for the following set of scores: 10, 15, 12, 18, 19, 16, 12? a b c d 10 ANS: C PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Application 40 What is the standard deviation for the following set of scores: 10, 15, 12, 18, 19, 16, 12? a 3.36 b 11.29 c 6.47 d 17.78 ANS: A PTS: DIF: Medium REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance COG: Application 41 What is the variance for the following set of scores: 10, 15, 12, 18, 19, 16, 12? a 3.36 b 11.29 c 6.47 d 17.18 ANS: B PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Application 42 What is the range for the following set of scores: 20, 24, 26, 22, 18, 16, 18? a 10 b 11 c 12 d 13 ANS: A PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Application 43 What is the standard deviation for the following set of scores: 20, 24, 26, 22, 18, 16, 18? a 12.95 b 3.60 c 6.55 d 24 ANS: B PTS: DIF: Medium REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance COG: Application 44 What is the variance for the following set of scores: 20, 24, 26, 22, 18, 16, 18? a 12.95 b 3.60 c 6.55 d 24 ANS: A PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Application 45 Which of the following sets of data has no variability? a 1, 2, 5, 4, b 7, 7, 7, 2, c 5, 5, 5, 5, d 0, 0, 0, 0, 10 ANS: C PTS: DIF: Easy REF: Why Understanding Variability Is Important OBJ: Why variability is valuable as a descriptive tool COG: Application 46 What is the standard deviation squared? a Range b Mean deviation c Variance d This cannot be computed ANS: C PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Knowledge 47 The variance of a group of scores is What is the standard deviation? a 3.5 b 18 c d 16 ANS: C PTS: DIF: Hard OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Application 48 If (X – M)2 = 235, and n = 29, what is s? a 8.10 b 8.39 c 2.90 d 43.64 ANS: C PTS: DIF: Hard REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance COG: Application 49 Which of the following must also be known in order to compute the standard deviation? a Mode b Mean c Range d Median ANS: B PTS: DIF: Easy REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance 50 Biased estimates can be used a To describe a sample COG: Knowledge b To describe a population c To describe a sample or a population d None of the above ANS: A PTS: DIF: Medium REF: Why n – 1? What’s Wrong With Just n? OBJ: Computing the range, standard deviation, and variance COG: Comprehension 51 Unbiased estimates can be used a To make sample estimates b To make population estimates c To make sample or population estimates d None of the above ANS: B PTS: DIF: Medium REF: Why n – 1? What’s Wrong With Just n? OBJ: Computing the range, standard deviation, and variance COG: Comprehension 52 When using sample estimates to estimate population parameters, you should use a Biased statistics b Unbiased statistics c Either biased or unbiased statistics d None of the above ANS: B PTS: DIF: Medium REF: Why n – 1? What’s Wrong With Just n? OBJ: Computing the range, standard deviation, and variance COG: Comprehension 53 As your sample size grows larger, the n - adjustment for the standard deviation has a a Greater impact on your calculation b Smaller impact on your calculation c The impact does not vary d This cannot be determined ANS: B PTS: DIF: Medium REF: Why n – 1? What’s Wrong With Just n? OBJ: Computing the range, standard deviation, and variance COG: Knowledge 54 As your sample size grows larger, your standard deviation will be a A more accurate estimate of the population b A less accurate estimate of the population c The accuracy will not change d This cannot be determined ANS: A PTS: DIF: Medium REF: Why n – 1? What’s Wrong With Just n? OBJ: Computing the range, standard deviation, and variance 55 If n = 24 and s = 1.56, what is the variance? a 2.43 b 1.25 c 0.06 d 0.0065 COG: Knowledge ANS: A PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Application 56 If you have a standard deviation of 5, your variance will be _ a b 25 c d 625 ANS: B PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Application 57 If you have a variance of 9, your standard deviation will be _ a b 81 c d ANS: C PTS: DIF: Medium REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance COG: Application 58 If (X – M)2 = 235, and n = 29, what is s2? a 8.10 b 8.39 c 2.90 d 43.64 ANS: B PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: Computing the Variance COG: Application 59 (X – M)2 = 235, and n = 29, what is s? a 11.3 b 23.5 c 8.39 d 2.90 ANS: D PTS: DIF: Medium REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance COG: Application 60 What is the mean for the following set of scores: 20, 24, 26, 22, 18, 16, 18? a 18 b 24 c 20.57 d 14.57 ANS: C PTS: DIF: Easy REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance TRUE/FALSE COG: Application The variance is more difficult to interpret than the standard deviation ANS: T PTS: DIF: Medium REF: The Standard Deviation Versus the Variance OBJ: Computing the range, standard deviation, and variance COG: Comprehension Unbiased estimates are considered to be less conservative estimates ANS: F PTS: DIF: Medium REF: Why n – 1? What’s Wrong With Just n? OBJ: Computing the range, standard deviation, and variance COG: Knowledge The standard deviation is sensitive to extreme scores ANS: T PTS: DIF: Medium OBJ: Computing the range, standard deviation, and variance REF: What’s the Big Deal? COG: Knowledge The exclusive range is more commonly used in research articles as compared with the inclusive range ANS: T PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: Computing the Range COG: Knowledge A greater standard deviation indicates less variance ANS: F PTS: DIF: Medium REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance COG: Comprehension A standard deviation equal to indicates no variance in your data ANS: T PTS: DIF: Easy OBJ: Computing the range, standard deviation, and variance REF: What’s the Big Deal? COG: Knowledge It is possible for a set of data to have no variability ANS: T PTS: DIF: Easy REF: Why Understanding Variability Is Important OBJ: Why variability is valuable as a descriptive tool COG: Comprehension SHORT ANSWER Define variability ANS: Variability reflects how scores differ from one another It is also a measure of how different scores are from the mean PTS: DIF: Medium REF: Why Understanding Variability Is Important OBJ: Why variability is valuable as a descriptive tool COG: Comprehension What are the strengths and limitations of the range? ANS: The range is the most general estimate of how far apart data points are from one another Its strength is that it is easy to compute while its limitation is that it does not provide insight into how each score deviates from each other or the mean PTS: DIF: Medium REF: Computing the Range OBJ: Computing the range, standard deviation, and variance COG: Comprehension What is the difference between the inclusive and exclusive range? ANS: The inclusive range is the highest score minus the lowest score plus one The exclusive range, which is more often used in journal articles, is the highest score minus the lowest score PTS: DIF: Medium REF: Computing the Range OBJ: Computing the range, standard deviation, and variance COG: Comprehension When computing the standard deviation, why are the deviations from the mean squared? ANS: In order to compute the standard deviation (the average distance a score is from the mean), you need an average of the deviations If you summed up the deviations from the mean, the sum would always be zero (arithmetic mean) By squaring the deviations, the negative signs disappear so that in the next step they can be summed without having the sum equal to zero, thus allowing the computations of the standard deviation to be completed PTS: DIF: Medium REF: Computing the Range OBJ: Computing the range, standard deviation, and variance COG: Comprehension Why is the square root taken when computing s? ANS: In order to compute the standard deviation, the deviations are squared The square root of the standard deviation is taken in order to return to the same units in which the values were originally measured PTS: DIF: Medium REF: Computing the Standard Deviation OBJ: Computing the range, standard deviation, and variance COG: Comprehension How does a biased standard deviation differ from an unbiased standard deviation? ANS: The biased standard deviation uses n in the denominator of its formula while the unbiased standard deviation uses n - in the denominator of its formula The unbiased standard deviation is used so as to not underestimate the population standard deviation PTS: DIF: Hard REF: Why n – 1? What’s Wrong With Just n? OBJ: Computing the range, standard deviation, and variance COG: Comprehension How are the standard deviation and the variance similar? How are they different? ANS: The standard deviation and variance are similar in that both are measures of variability and both are computed using similar formulas They are different because the standard deviation is stated in the original units from which it is derived while the variance is stated in squared units PTS: DIF: Medium REF: The Standard Deviation Versus the Variance OBJ: Computing the range, standard deviation, and variance COG: Comprehension Can the measures of central tendency and the measures of variability be used together to describe a set of scores? If so, how? ANS: Yes, the measures of central tendency and measures of variability can and should be used together to describe a distribution of scores The measures of central tendency describe the central points of a distribution while the measures of variability describe how spread out the scores are from one another and the mean PTS: DIF: Medium REF: Why Understanding Variability Is Important OBJ: Why variability is valuable as a descriptive tool COG: Comprehension What are the three measures of variability? Which is the most commonly reported? ANS: The three measures of variability are the range, the standard deviation, and the variance Although each is important, the standard deviation is the most useful and most commonly used index PTS: DIF: Easy REF: Why Understanding Variability Is Important OBJ: Computing the range, standard deviation, and variance COG: Knowledge ... estimates to estimate population parameters, you should use a Biased statistics b Unbiased statistics c Either biased or unbiased statistics d None of the above ANS: B PTS: DIF: Medium REF: Why n... Knowledge 38 Unbiased estimates a Are less conservative estimates of sample statistics b Are more conservative estimates of sample statistics c Are less conservative estimates of population parameters... standard deviation, and variance COG: Knowledge 26 Which of the following sets of scores has the greatest variability? a 7, 10, 11, 15, 19 b 7, 7, 8, 8, 10, 11 c 7, 7, 7, 7, 7, d 6, 6, 7, 7, 7, ANS: