Question 1

The sum of the differences between sample observations and the sample mean is equal to _______.
A)Zero
B)The mean deviation
C)The range
D)The standard deviation

Accepted Answer

This is the definition of the sample mean.

Question 2

For a sample of similar sized all-electric homes, the March electric bills were (to the nearest dollar): $212, $191, $176, $129, $106, $92, $108, $109, $103, $121, $175, and $194. What is the range?
A)$100
B)$130
C)$120
D)$112

Accepted Answer

The answer of For a sample of similar sized all-electric...

Question 3

What is the relationship between the variance and the standard deviation?
A)Variance is the square root of the standard deviation.
B)Variance is the square of the standard deviation.
C)Variance is twice the standard deviation.
D)There is no constant relationship between the variance and the standard deviation.

Accepted Answer

Variance is the average of squared differences from the mean while standard deviation is the square root of variance. Therefore, variance is the square of standard deviation.

Question 4

A disadvantage of using an arithmetic mean to summarize a set of data is that __________.
A)The arithmetic mean sometimes has two values
B)It can be used for interval and ratio data
C)It is always different from the median
D)It can be biased by one or two extremely small or large values

Accepted Answer

The arithmetic mean can be heavily influenced by extreme values in the data, leading to a biased representation of the central tendency. This is particularly true for small datasets.

Question 5

What is a disadvantage of the range as a measure of dispersion?
A)It is based on only two observations.
B)It can be distorted by a large mean.
C)It is not in the same units as the original data.
D)It has no disadvantage.

Accepted Answer

The range, as a measure of dispersion, is calculated as the difference between the maximum and minimum values in a dataset. This means it only takes into account the two extreme values, ignoring the distribution of all other data points, which can lead to a misleading representation of variability if the dataset is skewed or contains outliers.

Question 6

The weights (in thousands of kilograms) of seven shipping containers are 9.5, 10.3, 11.0, 10.4, 10.5, 11.2, and 9.2. What is the mean deviation?
A)0.543 kg
B)0.625 kg
C)0.53 kg
D)5.50 kg

Accepted Answer

Mean deviation = (Sum of absolute deviations from mean) / Number of valuesMean = (9.5 + 10.3 + 11.0 + 10.4 + 10.5 + 11.2 + 9.2) / 7 = 10.3Absolute deviations from mean: 0.8, 0.2, 0.7, 0.1, 0.2, 0.9, 1.1Sum of absolute deviations from mean = 3.7Mean deviation = 3.7 / 7 = 0.529 kg (approx)

Question 7

The mean, as a measure of central location, would be inappropriate for which one of the following?
A)Ages of adults at a senior citizen center
B)Incomes of lawyers
C)Number of pages in textbooks on statistics
D)Marital status of college students at a particular university

Accepted Answer

The mean would be inappropriate for the marital status of college students because marital status is a categorical variable, and the mean is typically used for quantitative variables. It would be more appropriate to use measures of frequency, such as percentages or proportions, to describe the marital status of college students. The mean could be used for the ages of adults, incomes of lawyers, and number of pages in textbooks because these are quantitative variables.

Question 8

The weights of a sample of crates ready for shipment to Moscow, Russia are (in kilograms): 103, 97, 101, 106, and 103. What is the mean deviation?
A)0 kg
B)6.9 kg
C)102.0 kg
D)2.4 kg

Accepted Answer

1. Find the mean:
Mean = (103 + 97 + 101 + 106 + 103) / 5 = 102 kg
2. Find the deviation of each weight from the mean:
|103 - 102| = 1
|97 - 102| = 5
|101 - 102| = 1
|106 - 102| = 4
|103 - 102| = 1
3. Find the mean of the deviations:
Mean deviation = (1 + 5 + 1 + 4 + 1) / 5 = 2.4 kg
Therefore, the answer is D.

Question 9

Which of the following measures of dispersion are based on deviations from the mean?
A)Variance
B)Standard deviation
C)Mean deviation
D)All apply

Accepted Answer

Variance, standard deviation, and mean deviation are all based on deviations from the mean. These measures of dispersion consider how much the data points deviate from the average value, providing insights into the variability of the dataset.

Question 10

Ten experts rated a newly developed chocolate chip cookie on a scale of 1 to 50. Their ratings were: 34, 35, 41, 28, 26, 29, 32, 36, 38, and 40. What is the mean deviation of the ratings?
A)8.00
B)4.12
C)12.67
D)0.75

Accepted Answer

To find the mean deviation, we first need to find the mean rating, which is:
(34+35+41+28+26+29+32+36+38+40)/10 = 34.9
Then, we find the deviation of each rating from the mean:
-0.9, 0.1, 6.1, -6.9, -8.9, -5.9, -2.9, 1.1, 3.1, and 5.1
We take the absolute value of each deviation and sum them up:
0.9+0.1+6.1+6.9+8.9+5.9+2.9+1.1+3.1+5.1 = 40
To find the mean deviation, we divide by the number of ratings, which is 10:
40/10 = 4
Therefore, the mean deviation of the ratings is 4. Answer choice B is the only one that matches this result.

Question 11

From the least difficult to the most difficult to compute, rank the measures of dispersion.
A)Mode, median, mean
B)Range, mean deviation, variance
C)Variance, mean deviation, range
D)There is no difference.

Accepted Answer

The measures of dispersion listed in option B from least difficult to most difficult to compute are: range, mean deviation, and variance. Range only requires the determination of the difference between the maximum and minimum values, which is a simple process. Mean deviation involves calculating the average of the absolute differences between each value and the mean. This is slightly more complicated than range, but still relatively easy. Variance, on the other hand, requires squaring the deviations from the mean, summing these squares, and dividing by the number of values. This is the most complex of the three measures listed in option B. Therefore, option B correctly ranks the measures of dispersion in order of increasing difficulty of computation.

Question 12

A purchasing agent for a trucking company is shopping for replacement tires for their trucks from two suppliers. The suppliers' prices are the same. However, Supplier A's tires have an average life of 60,000 miles with a standard deviation of 10,000 miles. Supplier B's tires have an average life of 60,000 miles with a standard deviation of 2,000 miles. Which of the following statements is true?
A)The two distributions of tire life are the same.
B)On average, Supplier A's tires have a longer life than Supplier B's tires.
C)The life of Supplier B's tire is more predictable than the life of Supplier A's tires.
D)The dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire life.

Accepted Answer

The standard deviation is a measure of the dispersion or variability in a dataset. A smaller standard deviation, like that of Supplier B's tires (2,000 miles), indicates that the tire life is more closely clustered around the mean (60,000 miles), making it more predictable compared to Supplier A's tires, which have a larger standard deviation (10,000 miles) and thus a wider spread of values.

Question 13

The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139, $136, $130, $136, $147, and $136. What is the range?
A)$0
B)$14
C)$52
D)$17

Accepted Answer

The answer of The following are the weekly amounts of...

Question 14

For the past week, a company's common stock closed with the following prices: $61.5, $62, $61.25, $60.875, and $61.5. What was the price range?
A)$1.250
B)$1.750
C)$1.125
D)$1.875

Accepted Answer

The price range is the difference between the highest and lowest prices. The highest price is $62 and the lowest is $60.875. The difference is $62 - $60.875 = $1.125.

Question 15

According to Chebyshev's Theorem, at least what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?
A)56%
B)95%
C)67%
D)100%

Accepted Answer

Chebyshev's Theorem states that for any data set, at least 1 - (1/k^2) of the observations will lie within k standard deviations of the mean, where k is any positive number greater than 1. Therefore, for k = 1.75, at least 1 - (1/1.75^2) = 1 - 0.327 = 0.673 or 67.3% of the observations will lie within plus and minus 1.75 standard deviations of the mean. Therefore, the best choice is C.

Question 16

A sample of the personnel files of eight male employees revealed that, during a six-month period, they were absent the following number of days: 2, 0, 6, 3, 10, 4, 1, and 2. What is the mean deviation (in days)?
A)1
B)0
C)3.125
D)2.375

Accepted Answer

The mean (average) number of days absent is calculated first: (2 + 0 + 6 + 3 + 10 + 4 + 1 + 2) / 8 = 28 / 8 = 3.5 days. Then, to find the mean deviation, calculate the absolute difference of each value from the mean and find their average: |2-3.5| + |0-3.5| + |6-3.5| + |3-3.5| + |10-3.5| + |4-3.5| + |1-3.5| + |2-3.5| = 1.5 + 3.5 + 2.5 + 0.5 + 6.5 + 0.5 + 2.5 + 1.5 = 19 / 8 = 2.375 days.

Question 17

What is a unique characteristic of the mean deviation?
A)It is based on only two observations.
B)It is based on deviations from the mean.
C)It uses absolute values.
D)It is only applied to skewed distributions.

Accepted Answer

The mean deviation uses absolute values to calculate deviations from the mean, which means it is unique compared to other measures of dispersion such as the range or standard deviation.

Question 18

If the variance of the "number of daily parking tickets issued is 100, the standard deviation is defined as the _____________.
A)"Number of daily parking tickets"
B)"Number of daily parking tickets" squared.
C)Absolute value of the variance of the "number of daily parking tickets"
D)Square root of the variance of the "number of daily parking tickets"

Accepted Answer

The standard deviation is defined as the square root of the variance. Therefore, the square root of 100 (the given variance) is the standard deviation, which is choice D.

Question 19

From the easiest to the hardest "ease of interpretation," rank the measures of dispersion.
A)Mode, median, mean
B)Range, mean deviation, variance
C)Variance, mean deviation, range
D)There is no difference.

Accepted Answer

Range is the easiest to interpret as it simply provides the difference between the maximum and minimum values. Mean deviation is slightly more complex but still easy to interpret as it provides the average deviation from the mean. Variance is the most difficult to interpret as it involves squaring the deviations from the mean, which makes it less intuitive. Therefore, option B is the best choice as it ranks the measures of dispersion in the order of increasing difficulty/ease of interpretation.

Question 20

Which measure of dispersion disregards the algebraic signs (plus and minus) of each difference between X and the mean?
A)Standard deviation
B)Mean deviation
C)Arithmetic mean
D)Variance

Accepted Answer

The mean deviation disregards the algebraic signs of each difference between X and the mean by taking the absolute value of each difference before averaging them. Standard deviation and variance both consider the signs of the differences. The arithmetic mean is not a measure of dispersion, but a measure of central tendency.

Quiz 3: Describing Data: Numerical Measures

The sum of the differences between sample observations and the sample mean is equal to _______.

For a sample of similar sized all-electric homes, the March electric bills were (to the nearest dollar) : $212, $191, $176, $129, $106, $92, $108, $109, $103, $121, $175, and $194. What is the range?

What is the relationship between the variance and the standard deviation?

A disadvantage of using an arithmetic mean to summarize a set of data is that __________.

What is a disadvantage of the range as a measure of dispersion?

The weights (in thousands of kilograms) of seven shipping containers are 9.5, 10.3, 11.0, 10.4, 10.5, 11.2, and 9.2. What is the mean deviation?

The mean, as a measure of central location, would be inappropriate for which one of the following?

The weights of a sample of crates ready for shipment to Moscow, Russia are (in kilograms) : 103, 97, 101, 106, and 103. What is the mean deviation?

Which of the following measures of dispersion are based on deviations from the mean?

Ten experts rated a newly developed chocolate chip cookie on a scale of 1 to 50. Their ratings were: 34, 35, 41, 28, 26, 29, 32, 36, 38, and 40. What is the mean deviation of the ratings?

From the least difficult to the most difficult to compute, rank the measures of dispersion.

The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139, $136, $130, $136, $147, and $136. What is the range?

For the past week, a company's common stock closed with the following prices: $61.5, $62, $61.25, $60.875, and $61.5. What was the price range?

According to Chebyshev's Theorem, at least what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?

A sample of the personnel files of eight male employees revealed that, during a six-month period, they were absent the following number of days: 2, 0, 6, 3, 10, 4, 1, and 2. What is the mean deviation (in days) ?

What is a unique characteristic of the mean deviation?

If the variance of the "number of daily parking tickets issued is 100, the standard deviation is defined as the _____________.

From the easiest to the hardest "ease of interpretation," rank the measures of dispersion.

Which measure of dispersion disregards the algebraic signs (plus and minus) of each difference between X and the mean?