Question 1

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$$ Compute the variance and standard deviation of the salaries.

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Question 2

The price-earnings ratios of a sample of stocks have a mean value of 13.5 and a standard deviation of 2. If the ratios have a mound-shaped distribution, what can we say about the proportion of ratios that fall between:
a. 11.5 and 15.5?
b. 9.5 and 17.5?
c. 7.5 and 19.5?

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Question 3

The mean of a sample of 15 measurements is 35.6. Suppose that the sample is enlarged to 16 measurements, by including one additional measurement having a value of 42. Find the mean of the sample of 16 measurements.

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Question 4

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$$ Compute the upper quartile.

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Question 5

The following data are the heights (in cm) of the 25 students in a business statistics class: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline 164 & 148 & 137 & 157 & 173 & 156 & 177 & 172 & 169 & 165 \
\hline 145 & 168 & 163 & 162 & 174 & 152 & 156 & 168 & 154 & 151 \
\hline 174 & 146 & 134 & 140 & 171 & & & & & \
\hline
\end{array}$$ Find the median height.

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The answer of The following data are the heights (in...

Question 6

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$$ Compute the range.

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The answer of The following data represent the salaries (in...

Question 7

A sample of eight observations of variables x and y is shown below: $$\begin{array} { | l | r | r | r | r | r | r | r | r | } 
\hline x & 5 & 3 & 7 & 9 & 2 & 4 & 6 & 8 \
\hline y & 20 & 23 & 15 & 11 & 27 & 21 & 17 & 14 \
\hline
\end{array}$$ Draw the scatter diagram and plot the least-squares line.

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The answer of A sample of eight observations of variables...

Question 8

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$$ Compute the coefficient of variation.

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Question 9

How is the value of the correlation coefficient r affected in each of the following cases?
a. Each x value is multiplied by 4.
b. Each x value is switched with the corresponding y value.
c. Each x value is increased by 2.

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Question 10

A sample of eight observations of variables x and y is shown below: $$\begin{array} { | l | r | r | r | r | r | r | r | r | } 
\hline x & 5 & 3 & 7 & 9 & 2 & 4 & 6 & 8 \
\hline y & 20 & 23 & 15 & 11 & 27 & 21 & 17 & 14 \
\hline
\end{array}$$ Calculate the covariance and the coefficient of correlation, and comment on the relationship between X and Y.

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Question 11

Given the following sample data: $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | c | } 
\hline x & 420 & 610 & 625 & 500 & 400 & 450 & 550 & 650 & 480 & 565 \
\hline y & 2.80 & 3.60 & 3.75 & 3.00 & 2.50 & 2.70 & 3.50 & 3.90 & 2.95 & 3.30 \
\hline
\end{array}$$ 
a. calculate the covariance and the correlation coefficient.
b. comment on the relationship between X and Y.
c. determine the least-squares line.
d. draw the scatter diagram and plot the least-squares line.

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Question 12

The following data are the heights (in cm) of the 25 students in a business statistics class: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline 164 & 148 & 137 & 157 & 173 & 156 & 177 & 172 & 169 & 165 \
\hline 145 & 168 & 163 & 162 & 174 & 152 & 156 & 168 & 154 & 151 \
\hline 174 & 146 & 134 & 140 & 171 & & & & & \
\hline
\end{array}$$ a. Compute the range of the data.
b. Compute the range approximation to the standard deviation of the data. (Hint: S $\approx$ Range/4.)

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Question 13

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$$ Compute the 90th percentile.

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The answer of The following data represent the salaries (in...

Question 14

a. Calculate the covariance and the coefficient of correlation for the following sample. $$\begin{array} { | l | r | r | r | r | r | } 
\hline x & 9 & 6 & 7 & 5 & 8 \
\hline y & 19 & 14 & 16 & 12 & 15 \
\hline
\end{array}$$ b. What do these statistics tell you about the relationship between X and Y?

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Question 15

Suppose that an analysis of a set of data reveals that $Q _ { 1 } = 45,$ $Q _ { 2 } = 85$ and $Q _ { 3 } = 105$ 
a. What do these statistics tell you about the shape of the distribution?
b. What can you say about the relative position of each of the observations 34, 84 and 104?
c. Calculate the interquartile range.
d. What does the interquartile range tell you about the data?

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Question 16

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$$ Compute the lower quartile.

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The answer of The following data represent the salaries (in...

Question 17

Consider the following population of measurements: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline 162 & 152 & 177 & 157 & 184 & 176 & 165 & 181 & 170 & 163 \
\hline
\end{array}$$ a. Compute the mean.
b. Compute the median.
c. Compute the variance and the standard deviation.

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Question 18

A supermarket has determined that daily demand for egg cartons has an approximate mound-shaped distribution, with a mean of 55 cartons and a standard deviation of 6 cartons.
a. For what percentage of days can we expect the number of cartons of eggs sold to be between 49 and 61?
b. For what percentage of days can we expect the number of cartons of eggs sold to be more than 2 standard deviations from the mean?
c. If the supermarket begins each morning with a stock of 77 cartons of eggs, for what percentage of days will there be an insufficient number of cartons to meet the demand?

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Question 19

A sample of 12 measurements has a mean of 25 and a standard deviation of 4. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 25.
a. Find the mean of the sample of 14 measurements.
b. Find the standard deviation of the sample of 14 measurements.

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Question 20

The following data are the heights (in cm) of the 25 students in a business statistics class: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline 164 & 148 & 137 & 157 & 173 & 156 & 177 & 172 & 169 & 165 \
\hline 145 & 168 & 163 & 162 & 174 & 152 & 156 & 168 & 154 & 151 \
\hline 174 & 146 & 134 & 140 & 171 & & & & & \
\hline
\end{array}$$ a. Compute the sample mean height.
b. Compute the sample variance.
c. Compute the sample standard deviation.

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Quiz 5: Numerical Descriptive Measures

The price-earnings ratios of a sample of stocks have a mean value of 13.5 and a standard deviation of 2. If the ratios have a mound-shaped distribution, what can we say about the proportion of ratios that fall between: a. 11.5 and 15.5? b. 9.5 and 17.5? c. 7.5 and 19.5?

The mean of a sample of 15 measurements is 35.6. Suppose that the sample is enlarged to 16 measurements, by including one additional measurement having a value of 42. Find the mean of the sample of 16 measurements.

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $\begin{array} { | l | l | l | l | l | l | l | } \hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \\\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \\\hline\end{array}$ Compute the range.

A sample of eight observations of variables x and y is shown below: $\begin{array} { | l | r | r | r | r | r | r | r | r | } \hline x & 5 & 3 & 7 & 9 & 2 & 4 & 6 & 8 \\\hline y & 20 & 23 & 15 & 11 & 27 & 21 & 17 & 14 \\\hline\end{array}$ Draw the scatter diagram and plot the least-squares line.

How is the value of the correlation coefficient r affected in each of the following cases? a. Each x value is multiplied by 4. b. Each x value is switched with the corresponding y value. c. Each x value is increased by 2.

a. Calculate the covariance and the coefficient of correlation for the following sample. $\begin{array} { | l | r | r | r | r | r | } \hline x & 9 & 6 & 7 & 5 & 8 \\\hline y & 19 & 14 & 16 & 12 & 15 \\\hline\end{array}$ b. What do these statistics tell you about the relationship between X and Y?

Consider the following population of measurements: $\begin{array} { | l | l | l | l | l | l | l | l | l | l | } \hline 162 & 152 & 177 & 157 & 184 & 176 & 165 & 181 & 170 & 163 \\\hline\end{array}$ a. Compute the mean. b. Compute the median. c. Compute the variance and the standard deviation.