Chapter 3 Business Statistics

True or False: In a set of numerical data, the value for Q2 is always halfway between Q1 and Q3.

False

True or False: The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 1.9.

False

True or False: The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 4.05.

False

The ordered array below represents the number of vitamin supplements sold by a health food store in a A sample of 16 days. 19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41 For this sample, the sum of the values is 448, and the sum of the squared differences between each value and the mean is 812. an Calculate the coefficient of variation.

0.27

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 7475 76 76 81 81 82 86 87 89 90 92 Calculate the coefficient of variation of the ages of the senior citizens.

13.16%

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 7475 76 76 81 81 82 86 87 89 90 92 Determine the interquartile range of the ages of the senior citizens.

15 years

You were told that the 1st, 2nd and 3rd quartiles of female students' weight at a major university are 95 lbs, 125 lbs, and 138 lbs. What percentage of the students weigh less than 95 lbs?

25%

You were told that the 1st, 2nd and 3rd quartiles of female students' weight at a major university are 95 lbs, 125 lbs, and 138 lbs. What percentage of the students weigh between 95 and 138 lbs?

50%

You were told that the 1st, 2nd and 3rd quartiles of female students' weight at a major university are 95 lbs, 125 lbs, and 138 lbs. What percentage of the students weigh more than 125 lbs?

50%

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 7475 76 76 81 81 82 86 87 89 90 92 Determine the first quartile of the ages of the senior citizens.

66 years

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 7475 76 76 81 81 82 86 87 89 90 92 Determine the median age of the senior citizens

73 years

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 7475 76 76 81 81 82 86 87 89 90 92 Calculate the arithmetic mean age of the senior citizens to the nearest hundredth of a year.

74.04 years

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 7475 76 76 81 81 82 86 87 89 90 92 Determine the third quartile of the ages of the senior citizens

81 years

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 7475 76 76 81 81 82 86 87 89 90 92 Calculate the standard deviation of the ages of of the senior citizens, correct to the nearest hundredth of a year.

9.74 years

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 7475 76 76 81 81 82 86 87 89 90 92 Calculate the variance of the ages of the senior citizens correct to the nearest hundredth of a year squared.

94.96 years^2

According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______percent of the observations will be contained within 1 standard deviation around the arithmetic mean. a) 68.26 b) 75.00 c) 88.89 d) 93.75

A

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 7475 76 76 81 81 82 86 87 89 90 92 Determine which of the following is the correct statement. a) One fourth of the senior citizens sampled are below 65.5 years of age. b) The middle 50% of the senior citizens sampled are between 65.5 and 73.0 years of age. c) The mean age of senior citizens sampled is 73.5 years of age. d) All of the above are correct.

A

Which of the following statements about the median is not true? a) It is more affected by extreme values than the arithmetic mean. b) It is a measure of central tendency. c) It is equal to Q2. d) It is equal to the mode in bell-shaped "normal" distributions.

A

In a right-skewed distribution a) the median equals the arithmetic mean. b) the median is less than the arithmetic mean. c) the median is greater than the arithmetic mean. d) none of the above.

B

In left-skewed distributions, which of the following is the correct statement? a) The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3. b) The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation. c) The distance from the smallest observation to Q2 is less than the distance from Q2 to the largest observation. d) The distance from Q1 to Q3 is twice the distance from the Q1 to Q2.

B

In right-skewed distributions, which of the following is the correct statement?a) The distance from Q1 to Q2 is greater than the distance from Q2 to Q3. b) The distance from Q1 to Q2 is less than the distance from Q2 to Q3. c) The arithmetic mean is less than the median. d) The mode is greater than the arithmetic mean.

B

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 7475 76 76 81 81 82 86 87 89 90 92 Identify which of the following is the correct statement. a) One fourth of the senior citizens sampled are below 64 years of age. b) The middle 50% of the senior citizens sampled are between 65.5 and 73.0 years of age. c) 25% of the senior citizens sampled are older than 81.5 years of age. d) All of the above are correct.

C

In a perfectly symmetrical distribution a) the range equals the interquartile range. b) the interquartile range equals the arithmetic mean. c) the median equals the arithmetic mean. d) the variance equals the standard deviation.

C

When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate: a) CV and range. b) arithmetic mean and standard deviation. c) interquartile range and median. d) variance and interquartile range.

C

Which measure of central tendency can be used for both numerical and categorical variables? a) Arithmetic mean. b) Median. c) Mode. d) Geometric mean.

C

Which of the following is NOT sensitive to extreme values? a) The range b) The standard deviation c) The interquartile range d) The coefficient of variation

C

Which of the following is sensitive to extreme values? a) The median b) The interquartile range c) The arithmetic mean d) The 1st quartile

C

According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______ percent of the observations will be contained within 3 standard deviations around the arithmetic mean. a) 68.26 b) 75.00 c) 95.0 d) 99.7

D

According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______percent of the observations will be contained within 2 standard deviations around the arithmetic mean. a) 68.26 b) 88.89 c) 93.75 d) 95.44

D

In a perfectly symmetrical bell-shaped "normal" distribution a) the arithmetic mean equals the median. b) the median equals the mode. c) the arithmetic mean equals the mode. d) All the above.

D

In perfectly symmetrical distributions, which of the following is NOT a correct statement? a) The distance from Q1 to Q2 equals to the distance from Q2 to Q3. b) The distance from the smallest observation to Q1 is the same as the distance from Q3 to the largest observation. c) The distance from the smallest observation to Q2 is the same as the distance from Q2 to the largest observation. d) The distance from Q1 to Q3 is half of the distance from the smallest to the largest observation.

D

The smaller the spread of scores around the arithmetic mean, a) the smaller the interquartile range. b) the smaller the standard deviation. c) the smaller the coefficient of variation. d) All the above.

D

Which of the following is NOT a measure of central tendency? a) The arithmetic mean. b) The geometric mean. c) The mode. d) The interquartile range.

D

Which of the following statistics is not a measure of central tendency? a) Arithmetic mean. b) Median. c) Mode. d) Q3.

D

In a sample of size 40, the sample mean is 15. In this case, the sum of all observations in the sample is ∑ Xi = 600.

True

The Z score of a value measures how many standard deviations the value is from the mean.

True

The Z scores can be used to identify outliers.

True

True or False: In a set of numerical data, the value for Q3 can never be smaller than the value for Q1

True

True or False: In right-skewed distributions, the distance from Q3 to the largest value is greater than the distance from the smallest observation to Q1.

True

True or False: The five-number summary consists of the smallest value, the first quartile, the median, the third quartile, and the largest value

True

The 12-month rate of returns over a three year period of a particular stock is 0.099, −0.289, and 0.089. The geometric mean rate of return per year for this stock is _______.

−5.24% or −0.0524