Question 1

Which Excel function would be least useful to calculate the quartiles for a column of data?
A)=STANDARDIZE
B)=PERCENTILE.EXC
C)=QUARTILE.EXC
D)=MODE

Accepted Answer

The answer of Which Excel function would be least useful...

Question 2

As a measure of variability,compared to the range,an advantage of the standard deviation is that it
A)is calculated easily through the use of a formula.
B)considers only the data values in the middle of the data array.
C)describes the distance between the highest and lowest values.
D)considers all data values.

Accepted Answer

The standard deviation considers all data values, making it a more comprehensive measure of variability than the range.

Question 3

The 25th percentile for waiting time in a doctor's office is 19 minutes.The 75th percentile is 31 minutes.Which is incorrect regarding the fences?
A)The upper inner fence is 49 minutes.
B)The upper outer fence is 67 minutes.
C)A waiting time of 45 minutes exceeds the upper inner fence.
D)A waiting time of 70 minutes would be an outlier.

Accepted Answer

The answer of The 25th percentile for waiting time in...

Question 4

Shown the spending by a sample of 50 breakfast customers of McDonald's.Which statement is least likely to be correct? 
A)The median is very close to the midhinge.
B)The median purchase is slightly less than $5.
C)About 75 percent of the customers spend less than $7.
D)The mean is a reasonable measure of center.

Accepted Answer

The mean may not be a reasonable measure of center for this data set because it is possible that there are some customers who have extremely high or low purchases, which can skew the mean. The other statements are plausible based on the given information.

Question 5

Which two statistics offer robust measures of center when outliers are present?
A)Mean and mode.
B)Median and trimmed mean.
C)Midrange and geometric mean.
D)Variance and standard deviation.

Accepted Answer

When outliers are present, mean and mode can be heavily impacted, making them unreliable measures of center. Midrange and geometric mean are also not robust measures of center. Therefore, the best choices are median and trimmed mean, as they are not influenced by extreme values and provide more reliable estimates of the central tendency of the data. Variance and standard deviation are measures of dispersion, not center.

Question 6

When using Chebyshev's Theorem,the minimum percentage of sample observations that will fall within two standard deviations of the mean will be ________ the percentage within two standard deviations if a normal distribution is assumed (Empirical Rule).
A)smaller than
B)greater than
C)the same as

Accepted Answer

Chebyshev's theorem is a general rule that applies to all types of probability distributions, including skewed distributions. It states that regardless of the shape of the distribution, at least 75% of the data observations will fall within two standard deviations of the mean, and at least 89% of the data observations will fall within three standard deviations of the mean. Thus, the minimum percentage of sample observations that will fall within two standard deviations of the mean using Chebyshev's Theorem is smaller than the percentage within two standard deviations if a normal distribution is assumed (Empirical Rule). The Empirical Rule states that for a normal distribution, approximately 68% of the data observations will fall within one standard deviation of the mean, approximately 95% will fall within two standard deviations of the mean, and approximately 99.7% will fall within three standard deviations of the mean.

Question 7

The median of 600,800,1000,1200 is
A)800
B)1000
C)900
D)950

Accepted Answer

The median is the average of the two middle numbers in an even set. Here, (800 + 1000) / 2 = 900.

Question 8

When a sample has an odd number of observations,the median is the
A)observation in the center of the data array.
B)average of the two observations in the center of the data array.
C)value of the most frequent observation.
D)average of Q1 and Q3.

Accepted Answer

When a sample has an odd number of observations, the median is the observation in the center of the data array. This is because when the data is arranged in order from smallest to largest, there will be an equal number of observations both above and below the median.

Question 9

Which Excel function is designed to calculate z = (x − μ)/σ for a column of data?
A)=STANDARDIZE
B)=NORM.DIST
C)=STDEV.P
D)=AVEDEV

Accepted Answer

The STANDARDIZE function is designed to calculate the standardized value (z-score) of a column of data by subtracting the mean (μ) and dividing by the standard deviation (σ). NORM.DIST is used to calculate the cumulative probability of a normal distribution, STDEV.P calculates the standard deviation of a population, and AVEDEV calculates the average deviation from the mean.

Question 10

The ________ shows the relationship between two variables.
A)box plot
B)bar chart
C)histogram
D)scatter plot

Accepted Answer

A scatter plot is specifically designed to display the relationship between two variables. It uses two-axis to plot points representing the observed values of the two variables, and the pattern of these points can reveal the nature and strength of their relationship.

Question 11

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 subtract the smallest value from the largest value: 69 - 3 = 66. 
To find the median, we first need to put the data in order: 3,6,7,17,17,23,51,69. The median is the middle value, which is 17. Therefore, the answer is C: 66 and 17.

Question 12

If the mean and median of a population are the same,then its distribution is
A)normal.
B)skewed.
C)symmetric.
D)uniform.

Accepted Answer

If the mean and median of a population are the same, then its distribution is symmetric. This means that the data is equally distributed around the center, resulting in the mean and median having the same value. This does not necessarily mean the data follows a specific distribution such as normal or uniform.

Question 13

Given a sample of three items (X = 4,6,5),which statement is incorrect?
A)The geometric mean is 5.2.
B)The standard deviation is 1.
C)The coefficient of variation is 20 percent.
D)The quartiles are useless.

Accepted Answer

The geometric mean of the sample (X = 4, 6, 5) is calculated as the nth root of the product of the numbers, which is not 5.2. The correct geometric mean is the cube root of (4*6*5) = cube root of 120, which is approximately 4.93, not 5.2.

Question 14

A sample of customers from Barnsboro National Bank shows an average account balance of $315 with a standard deviation of $87.A sample of customers from Wellington Savings and Loan shows an average account balance of $8350 with a standard deviation of $1800.Which statement about account balances is correct?
A)Barnsboro Bank has more variation.
B)Wellington S&L has more variation.
C)Both have the same variation.

Accepted Answer

The coefficient of variation (CV) is used to compare the relative variability between two datasets. For Barnsboro, CV = (87/315) * 100 ≈ 27.62%. For Wellington, CV = (1800/8350) * 100 ≈ 21.56%. Barnsboro Bank has a higher CV, indicating more relative variation.

Question 15

Based on daily measurements,Bob's weight has a mean of 200 pounds with a standard deviation of 16 pounds,while Mary's weight has a mean of 125 pounds with a standard deviation of 15 pounds.Who has the smaller relative variation?
A)Bob
B)Mary
C)They are the same.

Accepted Answer

Relative variation is measured by the coefficient of variation (CV), which is the standard deviation divided by the mean. Bob's CV is 16/200 = 0.08, while Mary's CV is 15/125 = 0.12. Bob has the smaller relative variation.

Question 16

Which distribution is least likely to be skewed to the right by high values?
A)Annual incomes of n passengers on a flight from New York to London
B)Weekend gambling losses of n customers at a major casino
C)Accident damage losses by n renters of an auto rental company
D)Cost of a plain McDonald's hamburger in n U.S.cities

Accepted Answer

Cost of a plain McDonald's hamburger in n U.S. cities is unlikely to have high values, and therefore unlikely to be skewed to the right. The other options involve variables where high values are possible, such as high incomes or large losses.

Question 17

VenalCo Market Research surveyed 50 individuals who recently purchased a certain CD,revealing the age distribution shown below.Which statement is least defensible? 
A)The mean age probably exceeds the median age.
B)The mode would be a reasonable measure of center.
C)The data are somewhat skewed to the left.
D)The CD is unlikely to appeal to retirees.

Accepted Answer

The answer of VenalCo Market Research surveyed 50 individuals who...

Question 18

Histograms are best used to
A)provide a visual estimate of the standard deviation.
B)show the quartiles of the data set.
C)assess the shape of the distribution.
D)reveal the interquartile range of the data set.

Accepted Answer

Histograms are used to assess the shape of the distribution, such as whether it is symmetric, skewed, bimodal, etc. They display the frequency or count of observations within intervals, allowing us to see patterns and trends in the data. They do not provide a visual estimate of the standard deviation, show the quartiles, or reveal the interquartile range of the data set.

Question 19

The 25th percentile for waiting time in a doctor's office is 19 minutes.The 75th percentile is 31 minutes.The interquartile range (IQR)is
A)12 minutes.
B)16 minutes.
C)22 minutes.
D)impossible to determine without knowing n.

Accepted Answer

The interquartile range (IQR) is calculated by subtracting the 25th percentile from the 75th percentile: 31 - 19 = 12 minutes.

Question 20

In the following data set {7,5,0,2,7,15,5,2,7,18,7,3,0},the value 7 is
A)the mean.
B)the mode.
C)both the mode and median.
D)both the mean and mode.

Accepted Answer

The value 7 appears the most frequently in the data set, making it the mode. It is not the mean or the median.

Quiz 4: Descriptive Statistics

Which Excel function would be least useful to calculate the quartiles for a column of data?

As a measure of variability,compared to the range,an advantage of the standard deviation is that it

The 25th percentile for waiting time in a doctor's office is 19 minutes.The 75th percentile is 31 minutes.Which is incorrect regarding the fences?

Shown the spending by a sample of 50 breakfast customers of McDonald's.Which statement is least likely to be correct?

Which two statistics offer robust measures of center when outliers are present?

When using Chebyshev's Theorem,the minimum percentage of sample observations that will fall within two standard deviations of the mean will be ________ the percentage within two standard deviations if a normal distribution is assumed (Empirical Rule) .

The median of 600,800,1000,1200 is

When a sample has an odd number of observations,the median is the

Which Excel function is designed to calculate z = (x − μ) /σ for a column of data?

The ________ shows the relationship between two variables.

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

If the mean and median of a population are the same,then its distribution is

Given a sample of three items (X = 4,6,5) ,which statement is incorrect?

Based on daily measurements,Bob's weight has a mean of 200 pounds with a standard deviation of 16 pounds,while Mary's weight has a mean of 125 pounds with a standard deviation of 15 pounds.Who has the smaller relative variation?

Which distribution is least likely to be skewed to the right by high values?

VenalCo Market Research surveyed 50 individuals who recently purchased a certain CD,revealing the age distribution shown below.Which statement is least defensible?

Histograms are best used to

The 25th percentile for waiting time in a doctor's office is 19 minutes.The 75th percentile is 31 minutes.The interquartile range (IQR) is

In the following data set {7,5,0,2,7,15,5,2,7,18,7,3,0},the value 7 is