Chapter 5- PY 211

9. the variance can best be thought of as the a) average of the squared deviations from the mean b) average absolute deviations from the mean c) average of the deviations from the median d) square the mean

a) average of the squared deviations from the mean

35. The disadvantage of using an interquartile range is that a) it discards too much of the data b) it removes outliers only extremely high in value c) the positive and negative deviations balance out d) it is disproportionately influenced by outliers

a) it discards too much of the data

21. As you increase the number of observations in a sample from 50 to 500, you are most likely to, a) leave the mean and standard deviation approximately unchanged b) increase the variability as the sample size increases c) decrease the variability as the sample size increases d) make the shape of the distribution more skewed

a) leave the mean and standard deviation approximately unchanged

28. The problem with measuring dispersion by merely averaging all the deviations between each score and the overall mean is that a) positive and negative deviations will balance out b) squared values make intuitive interpretation difficult c) dividing by (N-1) gives a biased statistic d) there are no problems with measuring dispersion this way

a) positive and negative deviations will balance out

24. If we know that a set of test scores has a mean of 75 and a standard deviation of 8, we would conclude that a) the average deviation form the mean is about 8 points b) the average person will have a score of 75 + 8 = 83 c) more people are above 75 than below it d) You can't tell anything about how scores lie relative to the mean

a) the average deviation form the mean is about 8 points

1. which of the following is NOT a measure of variability? a) the density b) the range c) the standard deviation d) the interquartile range

a) the density

36. Given the numbers 1, 2, and 3, the standard deviation is 1) 0 b) 1 c) 0.667 d) the square of the variance

b) 1

33. If the average adult male in the United States is 5'9'' tall, and the standard deviation for height is 2'', approximately how many adult males would you expect to be between 5'7'' and 5'11'' tall? a) 50% of them b) 66.7% of them c) 75% of them d) 90% of them

b) 66.7% of them

38. A "hinge" is another word for a) the median b) the quartile c) the range d) boundary

b) a quartile

10. What do we mean by an unbiased statistic? a) a statistic that equals the sample mean b) a statistic whose average is very stable from sample to sample c) a statistic used to measure racial diversity d) a statistic whose long range average is equal to the parameter it estimates

b) a statistic whose average is very stable from sample to sample

13. In a boxplot the width of the box encompasses a) all of the observed values b) all but the most extreme values c) approximately 50% of the observed values d) the center-most 10% of the values

b) all but the most extreme values

30. The equation mendian location +1/2 is used to calculate the a) median b) hinge location c) outer fence d) inner fences

b) hinge location

17. If the whiskers on a boxplot are much longer on the right than on the left, we would suspect that the distribution is a) positively skewed b) negatively skewed c) symmetric d) distorted

A) positively skewed

7. We generally like the standard deviation when we are trying to describe a sample of data because a) it is larger than the variance b) it allows for more intuitive interpretation with respect to the data than does the variance c) it is less biased than the variance d) all of the above

b) it allows for more intuitive interpretation with respect to the data than does the variance

40. We normally compute the variance using N-1 in the denominator because a) it is easier that way b) it leads to an unbiased estimate of the sample variance c) it leads to an unbiased estimate of the population variance d) it overestimates that population variance

b) it leads to an unbiased estimate of the sample variance

8. When calculating the standard deviation we divide by N-1 rather than N because the result is a) smaller b) less biased c) easier to interpret d) equal to the population mean

b) less biased

15. Data points at the extremes of the distribution have a) little effect on the variance b) more effect on the variance than scores at the center of the distribution c) are undoubtedly incorrect d) distort the usefulness of the medium

b) more effect on the variance than scores at the center of the distribution

20. If we multiply a set of data by a constant, such as concerting feet to inches, we will a) leave the mean and variance unaffected b) multiply the mean and the standard deviation by the constant c) multiply the mean by the constant but leave the standard deviation unchanged d) leave the mean unchanged but alter the standard deviation

b) multiply the mean and the standard deviation by the constant

16. Data points that lie outside the whiskers in a boxplot are often referred to as a) incorrect values b) outliers c) representative values d) deviates

b) outliers

12. The vertical line in the center of a box plot a) represents the sample mean b) represents the sample median c) serves to anchor the box d) can represent anything you want it to

b) represents the sample median

3. the US Census Bureau collected data on family composition and found that samples from different parts of the country gave very different results for the mean number of family members living in households. If all the data were combined to one data set, a) the standard deviation of number of family members would probably be very small b) the standard deviation of number of family members would probably me relatively high c) the interquartile range would be small d) the median would equal the mean

b) the standard deviation of number of family members would probably me relatively high

41. The population variance is a) an estimate of the sample variance b) usually an unknown that we try to estimate c) calculated exactly like the sample variance d) a biased estimate

b) usually an unknown that we try to estimate

29. A data set of intelligence scores was collected from high school seniors. The IQ scores ranged from 82 to 113. Which of the following is probably NOT a reasonable estimate of the standard deviation? a) 6.2 b) 4.7 c) 35.4 d) all of the above are reasonable estimates

c) 35.4

32. The interquartile range a) in the 50th percentile score in a data set b) contains as few as 25% of scores or as many as 75% of scores in a data set c) contains the middle 50% of scores in a data set d) is the same as the range

c) contains the middle 50% of scores in a data set

18. People in the stock market refer to a measure called the "standard deviation". although it is calculated somewhat differently from one discussed here. It is a good guess that this measure refers to a) riskiness of the stock b) the value of the stock c) how much the stock price is likely to fluctuate d) how much money you are likely to earn from buying that stock

c) how much the stock price is likely to fluctuate

4. If we eliminate the top and bottom 25% of the data and take the range of what remains we have the a) range b) adjusted range c) interquartile range d) quartile variance

c) interquartile range

42. Data points at the extremes of the distribution have a) little effect on the variance b) distort the usefulness of the median c) more effect on the variance than the scores at the center of the distribution d) are undoubtedly incorrect

c) more effect on the variance than the scores at the center of the distribution

27. Which of the following is NOT a method of describing data that reduces the role of outliers on the measurement of a data set's variability? a) interquartile range b) boxplot c) range d) trimmed statistics

c) range

2. Dispersion refers to a) the degree to which data cluster toward one end of the scale b) the centrality of the distribution c) the degree to which individual data points are distributed around the mean d) all of the above

c) the degree to which individual data points are distributed around the mean

19. Which of the following sets of data is likely to have the smallest standard deviation? a) the distribution of SAT scores for students from your high school b) the distribution of heights of students in an elementary school c) the grade point averages of students from your high school's honors biology class d) the amount that you and your friends pay for college tuition

c) the grade point averages of students from your high school's honors biology class

39. A boxplot is bettwe than a statistic such as the mean when your purpose is a) to describe the central tendency of a population b) the describe the variability of a population c) to understand what a distribution of data looks like d) it is only worthwhile if you care only about medians

c) to understand what a distribution of data looks like

23. The standard deviation for the numbers 8, 9, and 10 is a) -3.0 b) 0.0 c) 0.67 d) 1.0

d) 1.0

22. The university counseling center has treated a large number of students for depression. They find that the standard deviation of depression scores for their pool of students is substantially higher after treatment than before treatment. The most likely explanation is a) some students improved more than others b) some students improved substantially while others actually got worse c) depression therapy at the counseling center affects different students differently d) all of the above

d) all of the above

34. Errors that can lead to outliers can occur in a) measurement b) data recording c) data entry d) all of the above

d) all of the above

37. If I continue to draw observations from a population and recalculate the mean each time I add an observation, the mean will approach _____ as the sample size increases a) its expected value b) the true population mean c) the median of the population if the population is symmetric d) all of the above

d) all of the above

3. An outlier a) can be an extreme score b) can be an error that snuck into the data c) will never have a large influence on many measures of variability d) both a and b

d) both a and b

14. The whiskers in a boxplot a) always enclose all of the data points b) always run from the smaller inner fence to the larger inner fence c) encompasses the H-spread only d) contain all the data points outside the box except the outliers

d) contain all the data points outside the box except the outliers

5. A trimmed sample is one that a) has been distorted by lopping off the highest scores b) is strongly influenced by outliers c) in unrepresentative of what it purports to measure d) has been truncated equally at the two extremes

d) has been truncated equally at the two extremes

26. The range is a) the difference between the inner fences b) the H-spread c) not influenced very much by outliers d) the difference between the highest and lowest score

d) the difference between the highest and lowest score

11. The difference between s and σ is that σ is a) the value of the standard deviation in a sample b) the long range average of the variance over repeated sampling c) the biased estimate of s d) the value of the standard deviation in a population

d) the value of the standard deviation in a population

6. The population variance is a) an estimate of the sample variance b) calculated exactly like the sample variance c) a biased estimate d) usually an unknown that we try to estimate

d) usually an unknown that we try to estimate

25. You would obtain a negative value for the variance is a) all observations were at the mean b) the distribution is very negatively skewed c) the distribution is positively skewed d) you would never obtain a negative variance

d) you would never obtain a negative variance