Question 1

The standard deviation of the scores is:
A)0.304
B)1.333
C)1.744
D)1.838

Accepted Answer

The answer of The standard deviation of the scores is:
A)0.304
B)1.333
C)1.744
D)1.838
...

Question 2

The Empirical Rule states that the percentage of observations in a data set (providing that the data set has a bell-shaped and symmetric distribution)that fall within one standard deviation of their mean is approximately:
A)68%
B)75%
C)95%
D)99%

Accepted Answer

The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.

Question 3

The following ten scores were obtained on a 20-point quiz: 4,5,8,9,11,13,15,18,18,and 20.The teacher computed the usual descriptive measures of center (central tendency)and variability (dispersion)for these data,and then discovered an error was made.One of the 18s should have been a 16.Which of the following measures,calculated on the corrected data,would change from the original computation?
A)median
B)arithmetic mean
C)range
D)geometric mean

Accepted Answer

The arithmetic mean would change because it takes into account the value of every score, and changing one score would change the overall average. The median would not change because it is simply the middle value and is not influenced by extreme scores like the 16 or 20. The range would not change because it is simply the difference between the highest and lowest scores, and changing one score would not affect that difference. The geometric mean is not commonly used for this type of data, and would not change anyway because it involves multiplying the scores together and taking the nth root, not affected by a single changed score.

Question 4

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The following data represent a sample of 10 scores on a statistics quiz: 16,16,16,16,16,18,18,20,20,and 20.
-The median score is:
A)16
B)17
C)18
D)19

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 5

Which one of the values below represents a lower quartile for the data set 23,24,21,and 20?
A)22.0
B)22.5
C)20.25
D)23.5

Accepted Answer

The lower quartile is the median of the lower half of the data set. The data set can be ordered as 20, 21, 23, and 24. The lower half of the data set is 20 and 21. The median of 20 and 21 is 20.25.

Question 6

A college placement office conducted a survey of 100 engineers who had graduated from Stanford University.For these engineers,the mean salary was computed to be $72,000 with a standard deviation of $8,000.The percentage of these engineers who earn more than $96,000 or less than $48,000 is:
A)approximately 0%.
B)at least 5.6% (1/18 of the engineers).
C)at most 5.6% (1/18 of the engineers).
D)at most 11.1% (1/9 of the engineers).

Accepted Answer

We need to find the percentage of engineers who earn more than $96,000 or less than $48,000.

Using the empirical rule, we can say that approximately 68% of the engineers earn salaries between $64,000 ($72,000 - one standard deviation of $8,000) and $80,000 ($72,000 + one standard deviation of $8,000).

Using the same empirical rule, we can say that approximately 95% of the engineers earn salaries between $56,000 ($72,000 - two standard deviations of $8,000) and $88,000 ($72,000 + two standard deviations of $8,000).

Since $48,000 is more than two standard deviations below the mean salary, we can say that less than 2.5% of the engineers earn salaries less than $48,000.

Similarly, since $96,000 is more than two standard deviations above the mean salary, we can say that less than 2.5% of the engineers earn salaries more than $96,000.

Therefore, the percentage of engineers who earn more than $96,000 or less than $48,000 is at most 2.5% + 2.5% = 5%, which is equivalent to 5/100 or 1/20 or 1/9. The closest answer choice to this value is D, which states that the percentage is at most 11.1% (1/9 of the engineers).

Question 7

For any set of grouped or ungrouped data,which measures of central location always have only one value?
A)arithmetic mean and median
B)median and mode
C)mode and arithmetic mean
D)geometric mean and mode

Accepted Answer

The arithmetic mean (average) and median (middle value in an ordered list) each have only one value for any given set of data, regardless of whether the data is grouped or ungrouped. The mode, which is the most frequently occurring value, can have more than one value if the data set has more than one modal value. The geometric mean is not relevant to the question of uniqueness in the context of central location measures.

Question 8

The range of the scores is:
A)4
B)6
C)8
D)9

Accepted Answer

The answer of The range of the scores is:
A)4
B)6
C)8
D)9...

Question 9

The covariance of the following sample data of four (X,Y)pairs: (1,5),(2,10),(4,7),and (5,9)equals:
A)1.25
B)2.50
C)3.75
D)3.69

Accepted Answer

The answer of The covariance of the following sample data...

Question 10

Which of the following represents a disadvantage of using the sample range to measure spread or dispersion?
A)It produces spreads that are too large.
B)The sample range is not measured in the same units as the data.
C)The largest or smallest observation (or both)may be an outlier.
D)None of the above is correct.

Accepted Answer

The sample range is heavily influenced by outliers, especially when the largest or smallest observation (or both) is an outlier. This can lead to a misleading measure of spread or dispersion. The other answers are not accurate drawbacks of using the sample range as a measure of spread.

Question 11

According to the Empirical Rule,the percentage of observations in a data set (providing that the data set has a bell-shaped and symmetric distribution)that should fall within two standard deviations of their mean is approximately:
A)90%
B)95%
C)97.5%
D)100%

Accepted Answer

The Empirical Rule states that approximately 95% of the observations in a data set with a bell-shaped and symmetric distribution fall within two standard deviations of their mean. Therefore, B is the best choice.

Question 12

Which of the following statements is true?
A)The mean is a measure of the deviation in a data set.
B)The standard deviation is a measure of variability.
C)The range is a measure of central location.
D)The median is a measure of variability.

Accepted Answer

The standard deviation is a measure of variability, as it measures the spread of a data set around the mean. The mean is a measure of central location, so statement A is incorrect. The range is the difference between the maximum and minimum values in a data set, so statement C is incorrect. The median is a measure of central location, specifically the middle value when the data set is arranged in order, so statement D is incorrect.

Question 13

For which measure of central location will the sum of the deviations of each data value from that measure always be zero?
A)arithmetic mean
B)geometric mean
C)median
D)mode

Accepted Answer

The arithmetic mean is the only measure of central location for which the sum of the deviations of each data value from that measure will always be zero. This is because the arithmetic mean is calculated by summing all the values and dividing by the number of values, making it the balance point of the dataset.

Question 14

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The following data represent a sample of 10 scores on a statistics quiz: 16,16,16,16,16,18,18,20,20,and 20.
-The mean score is:
A)17.0
B)17.6
C)18.0
D)10.0

Accepted Answer

To find the mean score, we need to add up all the scores and divide by the number of scores (in this case, 10). 
(16 + 16 + 16 + 16 + 16 + 18 + 18 + 20 + 20 + 20)/10 = 176/10 = 17.6. Therefore, the correct answer is B.

Question 15

For a sample of size 5,if x₁- = -5,x₂ - = 9,x₃ - = -7,and x₄ - = -2,then the sample standard deviation is: A)5.639 B)6.782 C)6.066 D)6.305

Accepted Answer

The answer of For a sample of size 5,if x<sub>1...

Question 16

For any distribution,the percent of observations that lie within four standard deviations of the mean is:
A)93.75% or more.
B)93.75% or less.
C)6)25% or more.
D)6)25% or less.

Accepted Answer

For any distribution, Chebyshev's theorem states that at least 1-(1/k^2) of the observations will lie within k standard deviations of the mean. So, for k=4, at least 1-(1/4^2) = 1-0.0625 = 0.9375, or 93.75% of the observations will lie within 4 standard deviations of the mean. Therefore, the best choice is A, which states that the percent of observations that lie within four standard deviations of the mean is 93.75% or more.

Question 17

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The following data represent a sample of 10 scores on a statistics quiz: 16,16,16,16,16,18,18,20,20,and 20.
-The modal score is:
A)16
B)17
C)18
D)20

Accepted Answer

The mode is the value that appears most frequently in a data set. In this case, the score of 16 appears 5 times, which is more frequent than any other score, making it the modal score.

Question 18

Which of the following is used as a divisor in the sample variances²,where n is the sample size? A)n + 1 B)n C)n - 1 D)n - 2

Accepted Answer

The divisor in the sample variance formula is n-1, which is the degrees of freedom in the sample. This corrects for the bias in the estimation of the population variance based on the sample variance. Therefore, the best choice is C.

Question 19

The correlation coefficient of the following sample data of four (X,Y)pairs: (1,5),(2,10),(4,7),and (5,9)equals:
A)0.263
B)0.412
C)0.528
D)0.364

Accepted Answer

The answer of The correlation coefficient of the following sample...

Question 20

Which of the following statement is true?
A)The range is found by taking the difference between the high and low values and dividing that value by 2.
B)The interquartile range is found by taking the difference between the 1st and 3rd quartiles and dividing that value by 2.
C)The standard deviation is expressed in terms of the original units of measurement but the variance is not.
D)The values of the standard deviation may be either positive or negative,while the value of the variance will always be positive.

Accepted Answer

The standard deviation is indeed expressed in the original units of measurement, making comparisons and interpretations more intuitive, while the variance is expressed in the units squared, making it less directly interpretable in terms of the original data.

Quiz 2: Describing Data: Numerical

The standard deviation of the scores is:

The Empirical Rule states that the percentage of observations in a data set (providing that the data set has a bell-shaped and symmetric distribution) that fall within one standard deviation of their mean is approximately:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The following data represent a sample of 10 scores on a statistics quiz: 16,16,16,16,16,18,18,20,20,and 20. -The median score is:

Which one of the values below represents a lower quartile for the data set 23,24,21,and 20?

A college placement office conducted a survey of 100 engineers who had graduated from Stanford University.For these engineers,the mean salary was computed to be $72,000 with a standard deviation of $8,000.The percentage of these engineers who earn more than $96,000 or less than $48,000 is:

For any set of grouped or ungrouped data,which measures of central location always have only one value?

The range of the scores is:

The covariance of the following sample data of four (X,Y) pairs: (1,5) ,(2,10) ,(4,7) ,and (5,9) equals:

Which of the following represents a disadvantage of using the sample range to measure spread or dispersion?

According to the Empirical Rule,the percentage of observations in a data set (providing that the data set has a bell-shaped and symmetric distribution) that should fall within two standard deviations of their mean is approximately:

Which of the following statements is true?

For which measure of central location will the sum of the deviations of each data value from that measure always be zero?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The following data represent a sample of 10 scores on a statistics quiz: 16,16,16,16,16,18,18,20,20,and 20. -The mean score is:

For a sample of size 5,if x₁- = -5,x₂ - = 9,x₃ - = -7,and x₄ - = -2,then the sample standard deviation is:

For any distribution,the percent of observations that lie within four standard deviations of the mean is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The following data represent a sample of 10 scores on a statistics quiz: 16,16,16,16,16,18,18,20,20,and 20. -The modal score is:

Which of the following is used as a divisor in the sample variances²,where n is the sample size?

The correlation coefficient of the following sample data of four (X,Y) pairs: (1,5) ,(2,10) ,(4,7) ,and (5,9) equals:

Which of the following statement is true?