Question 1

A sample of 117 records of the selling price of homes from Feb 15 to Apr 30, 2018 was taken from the files maintained by the Albuquerque Board of Realtors.The following are summary statistics for the selling prices. $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \text { Variable } & \mathrm { N } & \text { Mearn } & \text { Mirirmum } & \text { Q1 } & \text { Mediarl } & \text { Q3 } & \text { Maxirmlum } \
\hline \text { Prices } & 117 & 106270 & 54000 & 77650 & 96000 & 121750 & 215000 \
\hline
\end{array}$$ From this we can conclude that,
A)There are no outliers
B)More homes were sold for greater than $121750 than for less than $77650
C)68% of the selling price of these homes is from $77650 to $121750
D)25% of the selling price of these homes is at least $121750
E)The distribution of selling price of these homes is negatively skewed.

Accepted Answer

The third quartile (Q3) represents the point below which 75% of the data fall, meaning 25% of the data are above this point. Since Q3 is $121750, 25% of the selling prices are at least $121750.

Question 2

Your company is testing a new auto engine in a race car.The race car is on a 2-mile track.If the first lap was exactly at 2 minutes, so that the average speed for the first lap was 1.00 mile per minute, what would be the time required for the second lap so that the overall average speed will be 4 miles per minute?
A)It's not possible to end up with an overall average speed of 4 miles per minute.
B)1.0 minute
C)0.8 minutes
D)0.6 minutes
E)0.4 minutes

Accepted Answer

To achieve an overall average speed of 4 miles per minute over 2 laps (4 miles), the total time needed would be 1 minute (4 miles / 4 miles per minute = 1 minute). Since the first lap already took 2 minutes, it's impossible to achieve this overall average speed, making any time for the second lap irrelevant to reaching the desired average.

Question 3

David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB.His staff report several statistics for teller training hours.The mean is 20 hours, the standard deviation is 5 hours, the median is 15 hours, and mode is 10 hours.The Pearsonian coefficient of skewness-or Pearson's second skewness coefficient, defined as (3 × (μ - median)/σ)-for teller training hours is __________.
A)6
B)1
C)3
D)4
E)0

Accepted Answer

The answer of David Desreumaux, VP of Human Resources of...

Question 4

A business analyst is considering a data set reflecting the number of products purchased at one time, there is a mean of 159 and a standard deviation of 43.2.Given that the data set the number of products purchased for 5,791 purchases and is mound shaped, the analyst would expect 68% of the data points to be ________.
A)between 115.8 and 202.2
B)less than 5,791
C)between 72.6 and 245.4
D)greater than 61
E)between 43.2 and 159

Accepted Answer

For a mound-shaped (normal) distribution, 68% of the data points lie within one standard deviation of the mean. The mean is 159, and one standard deviation is 43.2. Adding and subtracting one standard deviation from the mean gives the range 115.8 (159 - 43.2) to 202.2 (159 + 43.2).

Question 5

A statistics student has a mean score of 92 in the first 3 tests.Suppose there are a total of 4 tests and all of them have equal weight.You can also assume that there is no extra credit in the last test.What is the best possible final average this student can get?
A)96
B)95
C)94
D)93
E)there is not enough information to find out

Accepted Answer

The answer of A statistics student has a mean score...

Question 6

The mean life of a particular brand of light bulb is 1200 hours.If you know that at about 95% of this brand of bulbs will last between 1100 and 1300 hours, then what is the standard deviation of the light bulbs' life?
A)25
B)50
C)75
D)100
E)200

Accepted Answer

The range from 1100 to 1300 hours represents approximately 95% of the data, which corresponds to 2 standard deviations in a normal distribution. Therefore, the total range of 200 hours (1300 - 1100) is equal to 4 standard deviations, making one standard deviation 50 hours.

Question 7

An electrical component for one of the main products your company produces is specified to have an electrical impedance of 2.15 ohms.However, the manufacturing process is not perfect and there is some variation on the actual impedance of these components.A recent statistical study indicated that in fact, the impedances are normally distributed with a mean impedance of 2.15 ohms and a standard deviation of 0.05 ohms.When the impedance exceeds 2.25 ohms, the product malfunctions so that component must be rejected and replaced by one whose impedance is within the acceptable limit.If you need 1350 usable components, how many components should you order?
A)1608
B)1422
C)1421
D)1417
E)1384

Accepted Answer

The answer of An electrical component for one of the...

Question 8

A statistics student made the following grades on the first 6 tests: 76, 82, 92, 95, 79, 86.The total number of tests for the semester is 7.What could be her median score for the whole semester?
A)It's not possible to answer without knowing the score on the last test.
B)76
C)82
D)92
E)95

Accepted Answer

The answer of A statistics student made the following grades...

Question 9

After obtaining a large data set, a business analyst will first want to determine _________.
A)descriptive statistics of all variables
B)the standard deviation of key variables
C)only the mean of all variables
D)what other variables should be included in the data set
E)when the updated version of the data set will be available

Accepted Answer

The first step in analyzing a large data set is to understand the basic characteristics of the data, which is achieved through descriptive statistics. This includes measures like mean, median, mode, range, and standard deviation, providing a summary of the data set.

Question 10

You have computed the z score for a value.Then you realize that the actual standard deviation of the population is 25% larger than the one you used for computing the z value.Your corrected z value will be _______.
A)25% smaller than the original value
B)25% larger than the original value
C)75% smaller than the original value
D)20% larger than the original value
E)20% smaller than the original value

Accepted Answer

The z score is calculated as $z = \frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. If the actual standard deviation is 25% larger, the denominator in the z score calculation increases, making the z score smaller. A 25% increase in the denominator does not lead to a 25% decrease in the z score, but it does make the z score smaller. Among the given options, the one that correctly reflects a decrease in the z score due to an increase in the standard deviation is the option indicating the z score will be 20% smaller, as this option correctly captures the direction of change without specifying an exact proportional relationship.

Question 11

The mean life of a specialized essential electronic component in one of your company's main products is 80 months, and its standard deviation is 6 months.It is known that the life for this component is not normally distributed.We can conclude that at least 96% of these components will last between _______.
A)74 and 86 months
B)68 and 92 months
C)66 and 94 months
D)64 and 96 months
E)50 and 110 months

Accepted Answer

The answer of The mean life of a specialized essential...

Question 12

A statistics student made the following grades on the first 6 tests: 76, 82, 92, 95, 92, 86.The total number of tests for the semester is 7.If the median score for the whole semester was 92, what could not have been the score of the last test?
A)77
B)92
C)93
D)94
E)96

Accepted Answer

To find the median of 7 scores, the scores must be arranged in order, and the 4th score will be the median. The current scores are 76, 82, 86, 92, 92, 95. If the median is 92, the 4th score must be 92. Adding a score of 77 would make the scores 76, 77, 82, 86, 92, 92, 95, making the median 86, not 92. Thus, 77 cannot be the score of the last test.

Question 13

A business analyst is considering a data set reflecting the number of products purchased at one time, there is a minimum of 45 and a maximum of 61.Given that the data set the number of products purchased for 5,791 purchases, the number of values at the mode would be expected to be ________.
A)less than 45
B)a large number since there is little variation in the number of products purchased
C)a small number since there is little variation in the number of products purchased
D)greater than 61
E)greater than 5,791

Accepted Answer

The mode is the value that appears most frequently in a data set. Given the narrow range of 45 to 61, it's likely that one or a few specific values occur very frequently, leading to a large number of values at the mode.

Question 14

In its Industry Norms and Key Business Ratios, Dun & Bradstreet reported that Q₁, Q₂, and Q₃ for 2,037 gasoline service stations' sales to inventory ratios were 20.8, 33.4, and 53.8, respectively.From this we can conclude that ____________. A)68% of these service stations had sales to inventory ratios of 20.8 or less B)50% of these service stations had sales to inventory ratios of 33.4 or less C)50% of these service stations had sales to inventory ratios of 53.8 or more D)95% of these service stations had sales to inventory ratios of 33.4 or more E)99% of these service stations had sales to inventory ratios of 53.8 or more

Accepted Answer

The given codes Q₁, Q₂, and Q₃ represent the 10th, 50th, and 90th percentiles, respectively. The 50th percentile (median) value of 33.4 means that 50% of the stations had sales to inventory ratios of 33.4 or less.

Question 15

A company is reviewing the database of customer purchases over the past 3 years.Using descriptive statistics on this large data set, a business analyst found the following values. $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \text { Variable } & \text { Court } & \text { Mearl } & \text { MinirmurI } & \text { Ql } & \text { Mediar } & \text { Q3 } & \text { Maxirnuri } \
\hline \text { Purdhases } & 56,472 & 105.21 & 10.24 & 31.09 & 74.88 & 117.23 & 201.40 \
\hline
\end{array}$$ From this we can conclude that,
A)68% of these purchases are between $105.24 and $74.88
B)The distribution of these purchases is negatively skewed
C)50% of these purchases are between $31.04 and $117.23
D)50% of these purchases are less than $105.24
E)The distribution of these purchases is not skewed

Accepted Answer

The values for Q1 (31.09) and Q3 (117.23) indicate that 50% of the purchases are between these two values, which is the definition of the interquartile range (IQR).

Question 16

A box-and-whisker plot for last year's data is compared with a box-and-whisker plot for this year's data.The biggest change is that the median is moved from the left side of the box to the right side of the box.The other elements of the plot remained fairly constant.Based on this change, it can be concluded that ___________.
A)the data have become more positively skewed
B)the data are less skewed than in the previous year
C)the skew has not changed between the two years
D)the data have become more negatively skewed
E)the data are more skewed than in the previous year

Accepted Answer

When the median moves from the left side of the box to the right side, it indicates that the distribution has a longer tail on the left side, which is characteristic of a more negatively skewed distribution.

Question 17

A company is reviewing the database of customer purchases over the past 3 years.Using descriptive statistics on this large data set, a business analyst found the following values. $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \text { Variable } & \text { Court } & \text { Mearl } & \text { MinirmurI } & \text { Ql } & \text { Mediar } & \text { Q3 } & \text { Maxirnuri } \
\hline \text { Purdhases } & 56,472 & 105.21 & 10.24 & 31.09 & 74.88 & 117.23 & 201.40 \
\hline
\end{array}$$ From this we can conclude that,
A)68% of these purchases are between $105.24 and $74.88
B)The distribution of these purchases is negatively skewed
C)50% of these purchases are between $105.21 and $117.23
D)50% of these purchases are less than $105.24
E)More of these purchases were below the mean than above the mean

Accepted Answer

The answer of A company is reviewing the database of...

Question 18

A company is reviewing the database of customer purchases over the past 3 years.Using descriptive statistics on this large data set, a business analyst found the following values. $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \text { Variable } & \text { Court } & \text { Mearl } & \text { MinirmurI } & \text { Ql } & \text { Mediar } & \text { Q3 } & \text { Maxirnuri } \
\hline \text { Purdhases } & 56,472 & 105.21 & 10.24 & 31.09 & 74.88 & 117.23 & 201.40 \
\hline
\end{array}$$ From this we can conclude that,
A)95% of these purchases are between $105.24 and $74.88
B)The distribution of these purchases is negatively skewed
C)More of these purchases had values less than $74.88 than above that amount
D)The distribution of these purchases is positively skewed
E)The distribution of these purchases is not skewed

Accepted Answer

The distribution is positively skewed because the mean (105.21) is greater than the median (74.88), indicating a longer tail on the right side of the distribution.

Question 19

A business analyst is considering a data set reflecting the number of products purchased at one time, there is a minimum of 45 and a maximum of 61.Given that the data set the number of products purchased for 5,791 purchases, the range would be ________.
A)less than 45
B)53
C)5791
D)greater than 61
E)16

Accepted Answer

The range of a data set is calculated by subtracting the minimum value from the maximum value. In this case, the range is 61 - 45 = 16.

Question 20

If a data set is negatively skewed, which calculations cannot be used?
A)Business analytics
B)Chebyshev's theorem
C)Descriptive statistics
D)Measures of variance
E)Empirical rule

Accepted Answer

The Empirical Rule applies only to data sets with a bell-shaped (normal) distribution, and cannot be used for negatively skewed distributions.

Quiz 3: Descriptive Statistics

A statistics student has a mean score of 92 in the first 3 tests.Suppose there are a total of 4 tests and all of them have equal weight.You can also assume that there is no extra credit in the last test.What is the best possible final average this student can get?

The mean life of a particular brand of light bulb is 1200 hours.If you know that at about 95% of this brand of bulbs will last between 1100 and 1300 hours, then what is the standard deviation of the light bulbs' life?

A statistics student made the following grades on the first 6 tests: 76, 82, 92, 95, 79, 86.The total number of tests for the semester is 7.What could be her median score for the whole semester?

After obtaining a large data set, a business analyst will first want to determine _________.

You have computed the z score for a value.Then you realize that the actual standard deviation of the population is 25% larger than the one you used for computing the z value.Your corrected z value will be _______.

A statistics student made the following grades on the first 6 tests: 76, 82, 92, 95, 92, 86.The total number of tests for the semester is 7.If the median score for the whole semester was 92, what could not have been the score of the last test?

A business analyst is considering a data set reflecting the number of products purchased at one time, there is a minimum of 45 and a maximum of 61.Given that the data set the number of products purchased for 5,791 purchases, the number of values at the mode would be expected to be ________.

In its Industry Norms and Key Business Ratios, Dun & Bradstreet reported that Q1, Q2, and Q3 for 2,037 gasoline service stations' sales to inventory ratios were 20.8, 33.4, and 53.8, respectively.From this we can conclude that ____________.

A business analyst is considering a data set reflecting the number of products purchased at one time, there is a minimum of 45 and a maximum of 61.Given that the data set the number of products purchased for 5,791 purchases, the range would be ________.

If a data set is negatively skewed, which calculations cannot be used?

In its Industry Norms and Key Business Ratios, Dun & Bradstreet reported that Q₁, Q₂, and Q₃ for 2,037 gasoline service stations' sales to inventory ratios were 20.8, 33.4, and 53.8, respectively.From this we can conclude that ____________.