Question 1

Which is not true of an outlier?
A)It is likely to be from a different population.
B)It suggests an error in recording the data.
C)It is best discarded to get a better mean.
D)It is an anomaly that may tell the researcher something.

Accepted Answer

Outliers should not always be discarded because they can provide valuable information about the data, such as the presence of extreme values or unusual patterns. Removing outliers can also significantly affect the calculated mean and other statistical measures. Therefore, it is important to carefully examine and understand the nature and potential causes of outliers before deciding whether to exclude them from the analysis.

Question 2

Exam scores in a small class were 10, 10, 20, 20, 40, 60, 80, 80, 90, 100, 100. For this data set, which statement is incorrect concerning measures of center?
A)The median is 60.00.
B)The mode is not helpful.
C)The 5 percent trimmed mean would be awkward.
D)The geometric mean is 35.05.

Accepted Answer

The geometric mean is not 35.05; it is calculated differently and would be lower due to the presence of low scores like 10 and 20.

Question 3

Exam scores in a small class were 0, 50, 50, 70, 70, 80, 90, 90, 100, 100. For this data set, which statement is incorrect concerning measures of center?
A)The median is 70.
B)The mode is not helpful.
C)The geometric mean is useless.
D)The mean is 70.

Accepted Answer

The answer of Exam scores in a small class were...

Question 4

Chebyshev's Theorem:
A)applies to all samples.
B)applies only to samples from a normal population.
C)gives a narrower range of predictions than the Empirical Rule.
D)is based on Sturges' Rule for data classification.The strength of Chebyshev's Theorem is that it makes no assumption about normality, while the

Accepted Answer

Chebyshev's Theorem applies to all samples, regardless of their distribution. It provides a minimum percentage of data that falls within a specified number of standard deviations from the mean, making it a more conservative estimate than the Empirical Rule. Sturges' Rule is used for determining the number of classes in a histogram and is not related to Chebyshev's Theorem.

Question 5

Which is true of the kurtosis of a distribution?
A)A distribution that is flatter than a normal distribution (i.e., thicker tails) is mesokurtic.
B)A distribution that is more peaked than a normal distribution (i.e., thinner tails) is platykurtic.
C)It is risky to assess kurtosis if the sample size is less than 50.
D)The expected range of the kurtosis coefficient increases as n increases.

Accepted Answer

Kurtosis assessment can be unreliable with small sample sizes, such as less than 50, because the estimates of kurtosis can be significantly affected by the lack of data, leading to inaccurate representations of the distribution's tail heaviness.

Question 6

Which is a correct statement concerning the median? A)In a left-skewed distribution, we expect that the median will exceed the mean. B)The sum of the deviations around the median is zero. C)The median is an observed data value in any data set. D)The median is halfway between Q₁ and Q₃ on a box plot.

Accepted Answer

In a left-skewed distribution, the median is typically greater than the mean because the long tail to the left pulls the mean down more than it affects the median.

Question 7

Estimating the mean from grouped data will tend to be most accurate when:
A)observations are distributed uniformly within classes.
B)there are few classes with wide class limits.
C)the sample is not very large and bins are wide.
D)the standard deviation is large relative to the mean.

Accepted Answer

When observations are distributed uniformly within classes, the estimate of the mean from the grouped data tends to be more accurate as each observation contributes equally to the class mean. In contrast, when the observations are not uniformly distributed, or when there are few classes with wide class limits, the estimate of the mean may not be accurate. A large sample size and smaller bin widths also tend to improve the accuracy of estimating the mean from grouped data. The size of the standard deviation relative to the mean is not relevant to the accuracy of estimating the mean from grouped data.

Question 8

A population consists of the following data: 7, 11, 12, 18, 20, 22, 25. The population variance is:
A)6.07.
B)36.82.
C)5.16.
D)22.86.

Accepted Answer

To find the population variance, we first need to find the population mean, which is (7+11+12+18+20+22+25)/7 = 15. 
Then, we calculate the sum of the squared differences between each data point and the mean: (7-15)^2 + (11-15)^2 + (12-15)^2 + (18-15)^2 + (20-15)^2 + (22-15)^2 + (25-15)^2 = 668. 
Finally, we divide by the total number of data points to get the population variance: 668/7 = 95.43/7 = 13.63. 
So, the closest choice is B, which is 36.82 (rounded to two decimal places). Note that this is the sample variance equation with n replaced by N, the population size. However, in practice, we usually use the sample variance formula with n-1 in the denominator when we only have a sample of the population, rather than the entire population.

Question 9

John scored 35 on Prof. Johnson's exam (Q₁ = 70 and Q₃ = 80). Based on the fences, which is correct? A)John is unusual but not an outlier. B)John is an outlier. C)John is neither unusual nor an outlier. D)John is in the 30^th percentile.

Accepted Answer

Based on the fences, any value that falls below Q1-1.5(IQR) or above Q3+1.5(IQR) is considered an outlier. In this case, Q1=70 and Q3=80, so the IQR is 80-70=10. Therefore, the lower fence is 70-1.5(10)=55 and the upper fence is 80+1.5(10)=95. Since John's score of 35 is lower than the lower fence of 55, he is considered an outlier.

Question 10

Which of the following is not a valid description of an outlier? A)A data value beyond the outer fences B)A data value that is very unusual C)A data value that lies below Q₁ or above Q₃ D)A data value several standard deviations from the mean.

Accepted Answer

The correct notation for quartiles should be Q1 and Q3, not QS1U1B1 and QS1U1B3. The notation in choice C is incorrect and does not validly describe an outlier.

Question 11

John scored 85 on Prof. Hardtack's exam (Q₁ = 40 and Q₃ = 60). Based on the fences, which is correct? A)John is an extreme outlier. B)John is an outlier. C)John is not an outlier. D)John is in the 85^th percentile.

Accepted Answer

Without knowing the specific values of the fences, we can determine that John's score falls within the interquartile range (IQR), which means he is not an outlier. Therefore, we can eliminate choices A and B. Additionally, the given information does not allow us to determine John's percentile, so we can eliminate choice D. Therefore, the correct answer is choice C.

Question 12

Which is true of skewness?
A)In business data, positive skewness is unusual.
B)In a negatively skewed distribution, the mean is likely to exceed the median.
C)Skewness often is evidenced by one or more outliers.
D)The expected range of Excel's skewness coefficient increases as n increases.

Accepted Answer

Skewness is often evidenced by one or more outliers, as these outliers can pull the distribution in one direction, creating skewness.

Question 13

In a sample of 10,000 observations from a normal population, how many would you expect to lie beyond three standard deviations of the mean?
A)None of them
B)About 27
C)About 100
D)About 127

Accepted Answer

In a normal distribution, about 99.7% of the data falls within three standard deviations of the mean. This means that 0.3% of the data lies beyond three standard deviations from the mean. For 10,000 observations, 0.3% of 10,000 is 30. However, since the distribution is on both sides of the mean, it's slightly less, making the closest estimate about 27.

Question 14

The Excel formula for the standard deviation of a sample array named Data is:
A)=STDEV.S(Data).
B)=STANDEV(Data).
C)=STDEV.P(Data).
D)=SUM(Data)/(COUNT(Data)-1).

Accepted Answer

The formula for the standard deviation of a sample array in Excel is STDEV.S(Data). STDEV.P(Data) is used for a population array and SUM(Data)/(COUNT(Data)-1) is not the correct formula for standard deviation.

Question 15

Which is not true of the Empirical Rule?
A)It applies to any distribution.
B)It can be applied to fewer distributions than Chebyshev's Theorem.
C)It assumes that the distribution of data follows a bell-shaped, normal curve.
D)It predicts more observations within μ ± kσ than Chebyshev's Theorem.The

Accepted Answer

The Empirical Rule specifically applies to normally distributed data, which is a bell-shaped curve, making it not applicable to any distribution. Chebyshev's Theorem, on the other hand, applies to all distributions, making the Empirical Rule less universally applicable.

Question 16

Exam scores in a random sample of students were 0, 50, 50, 70, 70, 80, 90, 90, 90, 100. Which statement is incorrect?
A)The standard deviation is 29.61.
B)The data are slightly left-skewed.
C)The midrange and mean are almost the same.
D)The third quartile is 90.

Accepted Answer

The answer of Exam scores in a random sample of...

Question 17

Consider the following data: 6, 7, 17, 51, 3, 17, 23, and 69. The range and the median are:
A)69 and 17.5.
B)66 and 17.5.
C)66 and 17.
D)69 and 17.

Accepted Answer

To find the range, we need to subtract the smallest value (3) from the largest value (69):
69 - 3 = 66
Therefore, the range is 66.

To find the median, we need to first put the values in order from least to greatest:
3, 6, 7, 17, 17, 23, 51, 69

The median is the middle number. In this case, we have an even number of values, so we need to find the average of the two middle values:
(17 + 23) / 2 = 20

Therefore, the median is 20.

The correct answer is C because it gives both the correct range and median.

Question 18

For U.S. adult males, the mean height is 178 cm with a standard deviation of 8 cm and the mean weight is 84 kg with a standard deviation of 8 kg. Elmer is 170 cm tall and weighs 70 kg. It is most nearly correct to say that:
A)Elmer's weight is more unusual than his height.
B)Elmer is heavier than he is tall.
C)Height and weight have the same degree of variation.
D)Height has more variation than weight.

Accepted Answer

To determine which characteristic is more unusual, we need to compare Elmer's height and weight to the mean and standard deviation of their respective distributions. We can use z-scores to do this:

z-score for Elmer's height = (170 - 178) / 8 = -1.00
z-score for Elmer's weight = (70 - 84) / 8 = -1.75

Both z-scores indicate that Elmer is below the mean for height and weight, but the z-score for weight is more negative than the z-score for height. This means that Elmer's weight is further from the mean and therefore more unusual than his height. Thus, choice A is the correct answer.

Question 19

Which statement is true?
A)With nominal data we can find the mode.
B)Outliers distort the mean but not the standard deviation.
C)Business and economic data are rarely skewed to the right.
D)If we sample a normal population, the sample skewness coefficient is exactly 0.

Accepted Answer

Nominal data is categorical data that can be counted and mode can be calculated as it is the most frequently occurring category.

Answer: B 
 Outliers can distort the mean as it is sensitive to extreme values. However, the standard deviation takes into account all values and is less affected by outliers.

Answer: None of them
 Skewness is a measure of asymmetry, and it is possible for business and economic data to be either skewed to the left or right. Additionally, if we sample a normal population, the sample skewness coefficient may not be exactly 0, as it depends on the sample size and the particular data.

Question 20

If samples are from a normal distribution with μ = 100 and σ = 10, we expect:
A)about 68 percent of the data within 90 to 110.
B)almost all the data within 80 to 120.
C)about 95 percent of the data within 70 to 130.
D)about half the data to exceed 75.

Accepted Answer

According to the empirical rule, about 68% of data from a normal distribution falls within one standard deviation (σ) of the mean (μ). Here, μ = 100 and σ = 10, so 90 to 110 is within one standard deviation.

Quiz 4: Descriptive Statistics

Which is not true of an outlier?

Exam scores in a small class were 10, 10, 20, 20, 40, 60, 80, 80, 90, 100, 100. For this data set, which statement is incorrect concerning measures of center?

Exam scores in a small class were 0, 50, 50, 70, 70, 80, 90, 90, 100, 100. For this data set, which statement is incorrect concerning measures of center?

Chebyshev's Theorem:

Which is true of the kurtosis of a distribution?

Which is a correct statement concerning the median?

Estimating the mean from grouped data will tend to be most accurate when:

A population consists of the following data: 7, 11, 12, 18, 20, 22, 25. The population variance is:

John scored 35 on Prof. Johnson's exam (Q₁ = 70 and Q₃ = 80) . Based on the fences, which is correct?

Which of the following is not a valid description of an outlier?

John scored 85 on Prof. Hardtack's exam (Q₁ = 40 and Q₃ = 60) . Based on the fences, which is correct?

Which is true of skewness?

In a sample of 10,000 observations from a normal population, how many would you expect to lie beyond three standard deviations of the mean?

The Excel formula for the standard deviation of a sample array named Data is:

Which is not true of the Empirical Rule?

Exam scores in a random sample of students were 0, 50, 50, 70, 70, 80, 90, 90, 90, 100. Which statement is incorrect?

Consider the following data: 6, 7, 17, 51, 3, 17, 23, and 69. The range and the median are:

For U.S. adult males, the mean height is 178 cm with a standard deviation of 8 cm and the mean weight is 84 kg with a standard deviation of 8 kg. Elmer is 170 cm tall and weighs 70 kg. It is most nearly correct to say that:

Which statement is true?

If samples are from a normal distribution with μ = 100 and σ = 10, we expect: