Question 1

Patient survival times after a certain type of surgery have a very right-skewed distribution due to a few high outliers. Consequently, which statement is most likely to be correct?
A)Median > Midrange
B)Mean < Median
C)Mean > Midrange
D)Mean > Trimmed Mean

Accepted Answer

In a right-skewed distribution, the mean is pulled towards the higher values by the outliers, making it larger than the trimmed mean, which reduces the impact of outliers by removing a percentage of the highest and lowest values.

Question 2

Outliers are indicated using fences on a
A)box plot.
B)dot plot.
C)histogram.
D)Pareto chart.

Accepted Answer

Outliers are typically identified and represented using fences on a box plot, where the fences are drawn based on the interquartile range (IQR) and any data points that lie outside of the fences are considered outliers. Dot plots and histograms can also show outliers, but they do not have specific methods for identifying and marking them. Pareto charts are used for displaying frequency distributions of categorical data and do not typically include information about outliers.

Question 3

Twelve randomly chosen students were asked how many times they had missed class during a certain semester, with this result: 3, 2, 1, 2, 1, 5, 9, 1, 2, 3, 3, 10. The median is:
A)7.0.
B)3.0.
C)3.5.
D)2.5.

Accepted Answer

To find the median, first arrange the numbers in order: 1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 9, 10. The median is the average of the 6th and 7th numbers: (2 + 3) / 2 = 2.5.

Question 4

Twelve randomly chosen students were asked how many times they had missed class during a certain semester, with this result: 3, 2, 1, 2, 1, 5, 9, 1, 2, 3, 3, 10. The geometric mean is:
A) $\sqrt [ 12 ] { 42 }$
B)2.604
C)1.517
D) $\sqrt [ 2 ] { 97200 }$

Accepted Answer

The formula for geometric mean is:
gm = (x1 * x2 * ... * xn)^(1/n)

Using the given values, we get:

gm = (3 * 2 * 1 * 2 * 1 * 5 * 9 * 1 * 2 * 3 * 3 * 10)^(1/12)
gm = (4860)^(1/12)
gm = 2.604

Therefore, the best choice is B.

Question 5

Which is a characteristic of the standard deviation?
A)It is not greatly affected by outliers.
B)It is measured in the same units as the mean.
C)It measures dispersion around the median.
D)It has a natural, concrete meaning.

Accepted Answer

The standard deviation is measured in the same units as the mean, making it a useful measure for comparing the variability of different datasets that are measured in different units.

Answer: A 
 The standard deviation is relatively robust to the influence of outliers, meaning that extreme values in the dataset will not disproportionately affect its value.

Answer: C and D 
 These statements are both incorrect. The standard deviation is not a measure of dispersion around the median, and it does not have a natural, concrete meaning in and of itself.

Question 6

So far this year, stock A has had a mean price of $6.58 per share with a standard deviation of $1.88, while stock B has had a mean price of $10.57 per share with a standard deviation of $3.02. Which stock is more volatile?
A)Stock A
B)Stock B
C)They are the same.

Accepted Answer

The answer of So far this year, stock A has...

Question 7

Twelve randomly chosen students were asked how many times they had missed class during a certain semester, with this result: 2, 1, 5, 1, 1, 3, 4, 3, 1, 1, 5, 18. For this sample, the geometric mean is:
A)2.158.
B)1.545.
C)2.376.
D)3.017.

Accepted Answer

The answer of Twelve randomly chosen students were asked how...

Question 8

Three randomly chosen California students were asked how many times they drove to Mexico last year. Their replies were 4, 5, 6. The geometric mean is:
A)3.87.
B)5.00.
C)5.42.
D)4.93.

Accepted Answer

The answer of Three randomly chosen California students were asked...

Question 9

The quartiles of a distribution are most clearly revealed in which display?
A)Box plot
B)Scatter plot
C)Histogram
D)Dot plot

Accepted Answer

The quartiles, which divide a distribution into four equal parts, are most clearly displayed in a box plot. The box represents the middle 50% of the data and the horizontal line inside the box represents the median. The bottom and top of the box represent the first and third quartiles, respectively. Thus, a box plot is the best choice for displaying quartiles.

Question 10

Twelve randomly chosen students were asked how many times they had missed class during a certain semester, with this result: 2, 1, 5, 1, 1, 3, 4, 3, 1, 1, 5, 18. For this sample, the median is:
A)2.
B)3.
C)3.5.
D)2.5.

Accepted Answer

To find the median, first, arrange the numbers in ascending order: 1, 1, 1, 1, 1, 2, 3, 3, 4, 5, 5, 18. Since there are 12 numbers, the median is the average of the 6th and 7th numbers: (2 + 3)/2 = 2.5.

Question 11

One disadvantage of the range is that:
A)only extreme values are used in its calculation.
B)it is expressed in different units than the mean.
C)it does not exist for some data sets.
D)it is undefined if any X values are 0 or negative.

Accepted Answer

The range is calculated as the difference between the maximum and minimum values in a data set, meaning it only considers these two extreme values and not any of the values in between.

Question 12

Three randomly chosen Seattle students were asked how many round trips they made to Canada last year. Their replies were 3, 4, 5. The geometric mean is:
A)3.877.
B)4.000.
C)3.915.
D)4.422.

Accepted Answer

To find the geometric mean, we need to multiply the numbers and then take the nth root, where n is the number of values. 
So, the product of the values is: 3*4*5=60 
And the cube root of 60 is approximately 3.915. Therefore, the answer is C.

Question 13

Here are statistics on order sizes of Megalith Construction Supply's shipments of two kinds of construction materials last year. $$\begin{array} { l c r } 
& \text { Girders } & \text { Rivets } \
\text { Mean } & 160 & 2800 \
\text { Std. Dev. } & 48 & 702
\end{array}$$ Which order sizes have greater variability?
A)Girders
B)Rivets
C)They are the same.
D)Cannot be determined without knowing n $\overline { X ^ { * } }$ $\overline { X ^ { * } }$

Accepted Answer

Variability is best assessed relative to the mean of the distribution, which is done through the coefficient of variation (CV = standard deviation / mean). For girders, CV = 48 / 160 = 0.3. For rivets, CV = 702 / 2800 = 0.25. Girders have a higher CV, indicating greater variability relative to their mean.

Question 14

Which statistics offer robust (resistant to outliers) measures of center?
A)Mean, midrange, mode.
B)Median, midhinge, trimmed mean.
C)Trimmed mean, midrange, midhinge.
D)Mean, mode, quartiles.

Accepted Answer

The median, midhinge, and trimmed mean are all robust measures of center as they are not influenced by outliers. The median is the most commonly used robust measure of center and is simply the middle value when the data is arranged in order. The midhinge is calculated by finding the average of the first and third quartiles, which makes it less sensitive to extreme values. The trimmed mean involves removing a certain percentage of outliers from both ends of the data set, which further reduces the impact of extreme values. Therefore, option B is the best choice.

Question 15

The Empirical Rule says that:
A)most business data sets are normally distributed.
B)outliers are within three standard deviations of the mean.
C)in most business data we expect the mean and median to be similar.
D)about 32 percent of the data are beyond one standard deviation from the mean.The

Accepted Answer

The Empirical Rule states that approximately 68% of data in a normal distribution lies within one standard deviation of the mean, leaving about 32% beyond one standard deviation.

Question 16

Which is not a measure of variability?
A)Mean absolute deviation (MAD)
B)Range
C)Coefficient of variation
D)Trimmed mean

Accepted Answer

Trimmed mean is not a measure of variability. It is a measure of central tendency, like mean or median. The other three options, MAD, range, and coefficient of variation, are all measures of variability.

Question 17

Three randomly chosen Colorado students were asked how many times they went rock climbing last month. Their replies were 5, 6, 7. The standard deviation is:
A)1.212.
B)0.816.
C)1.000.
D)1.056.

Accepted Answer

The answer of Three randomly chosen Colorado students were asked...

Question 18

Twelve randomly chosen students were asked how many times they had missed class during a certain semester, with this result: 2, 1, 5, 1, 1, 3, 4, 3, 1, 1, 5, 18. For this sample, which measure of center is least representative of the "typical" student?
A)Mean
B)Median
C)Mode
D)Midrange

Accepted Answer

The midrange is the average of the maximum and minimum values in the data set, which in this case is (18+1)/2 = 9.5. However, the value of 18 is an outlier and is much larger than the rest of the values. Therefore, the midrange is not a good measure of center for this sample as it is heavily influenced by the extreme value. The mean, median, and mode are all better measures of center for this data set.

Question 19

The values of x_min and x_max can be inferred accurately except in a: A)box plot. B)dot plot. C)histogram. D)scatter plot.

Accepted Answer

In a histogram, the exact values of x_min and x_max cannot be determined because the data is grouped into bins, and the precise values within each bin are not shown.

Question 20

Which of the following statements is likely to be true?
A)The median personal income of California taxpayers would probably be near the mean.
B)The interquartile range offers a measure of income inequality among California residents.
C)For income, the sum of squared deviations about the mean is negative about half the time.
D)For personal incomes in California, outliers in either tail would be equally likely.

Accepted Answer

The interquartile range is a measure of the spread of data that is resistant to outliers, making it a good measure for income inequality. The median and mean income may not necessarily be near each other, as income distribution is often skewed. The sum of squared deviations about the mean cannot be negative, as it is always a non-negative quantity. Outliers in personal incomes in California are not equally likely in either tail.

Quiz 4: Descriptive Statistics

Patient survival times after a certain type of surgery have a very right-skewed distribution due to a few high outliers. Consequently, which statement is most likely to be correct?

Outliers are indicated using fences on a

Twelve randomly chosen students were asked how many times they had missed class during a certain semester, with this result: 3, 2, 1, 2, 1, 5, 9, 1, 2, 3, 3, 10. The median is:

Twelve randomly chosen students were asked how many times they had missed class during a certain semester, with this result: 3, 2, 1, 2, 1, 5, 9, 1, 2, 3, 3, 10. The geometric mean is:

Which is a characteristic of the standard deviation?

So far this year, stock A has had a mean price of $6.58 per share with a standard deviation of $1.88, while stock B has had a mean price of $10.57 per share with a standard deviation of $3.02. Which stock is more volatile?

Twelve randomly chosen students were asked how many times they had missed class during a certain semester, with this result: 2, 1, 5, 1, 1, 3, 4, 3, 1, 1, 5, 18. For this sample, the geometric mean is:

Three randomly chosen California students were asked how many times they drove to Mexico last year. Their replies were 4, 5, 6. The geometric mean is:

The quartiles of a distribution are most clearly revealed in which display?

Twelve randomly chosen students were asked how many times they had missed class during a certain semester, with this result: 2, 1, 5, 1, 1, 3, 4, 3, 1, 1, 5, 18. For this sample, the median is:

One disadvantage of the range is that:

Three randomly chosen Seattle students were asked how many round trips they made to Canada last year. Their replies were 3, 4, 5. The geometric mean is:

Which statistics offer robust (resistant to outliers) measures of center?

The Empirical Rule says that:

Which is not a measure of variability?

Three randomly chosen Colorado students were asked how many times they went rock climbing last month. Their replies were 5, 6, 7. The standard deviation is:

Twelve randomly chosen students were asked how many times they had missed class during a certain semester, with this result: 2, 1, 5, 1, 1, 3, 4, 3, 1, 1, 5, 18. For this sample, which measure of center is least representative of the "typical" student?

The values of xmin and xmax can be inferred accurately except in a:

Which of the following statements is likely to be true?

The values of x_min and x_max can be inferred accurately except in a: