TO PLOT OR NOT TO PLOT: AN EXERCISE ON UNDERSTANDING
AND COMPARING DATASETS CASE STUDY SOLUTION
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SYNOPSIS
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As managers face a flood of data, it is very important that they effectively analyze and interpret the available
data to make decisions. Plotting data will help them in their analysis and interpretation of raw data. The
same is true for students in business programs. However, students in business programs (and managers)
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often do not see the importance of plotting data.
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This case addresses through a typical classroom scenario how data is presented and the benefits of plotting
data. Compared with displaying basic summary statistics like first-order and second-order moments,
plotting data is almost always equally informative or more so. Though summary statistics are often useful
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to characterize a dataset and distinguish among datasets, the exercise of plotting data can reveal some
So
The Case Solution Starts From page 4
,• Understand the importance in data analysis and interpretation of plotting the data
• Demonstrate the applications of plotting the graphs
• Understand mean, standard deviation, and regression coefficients
• Demonstrate the concept of the Anscombe quartet
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ASSIGNMENT QUESTIONS
1. For the data presented in AQ Data File, calculate the mean and standard deviation of x1 to x4 and y1 to
y4. What are your observations?
2. Calculate the correlation between Xi and Yi for all four samples. What are your observations?
3. Perform regressions of Yi on Xi for all four samples. What are your observations?
4. Based on your observations for the previous three questions, do you think the relationships between Xi
and Yi are the same in all four samples? How would you validate your conclusion? Do statistical tests
support your conclusion?
5. Now plot the data for each pair of variables i.e. (X1, Y1) and (X2, Y2), (X3, Y3) and (X4, Y4)as scatter
plots. Do you find any contradiction with your previous observations? If yes, how can you reconcile?
The Case Solution Starts From page 4
, ANALYSIS
1. For the data presented in AQ Data File, calculate the mean and standard deviation of x1 to x4
and y1 to y4. What are your observations?
As shown in the table below, the mean for the X variables x1 to x4 is 9 and the standard deviation for each
variable is 3.32. The mean for the Y variables from y1 to y4 is 7.50 for each variable and the standard deviation
is 2.03. We can see that the means and standard deviations are the same for each of the four different datasets.
Variable Mean Standard deviation
x1 9 3.32
x2 9 3.32
x3 9 3.32
x4 9 3.32
y1 7.50 2.03
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y2 7.50 2.03
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y3 7.50 2.03
y4 7.50 2.03
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The Case Solution Starts From page 4
AND COMPARING DATASETS CASE STUDY SOLUTION
e
pl
SYNOPSIS
m
Sa
As managers face a flood of data, it is very important that they effectively analyze and interpret the available
data to make decisions. Plotting data will help them in their analysis and interpretation of raw data. The
same is true for students in business programs. However, students in business programs (and managers)
n
often do not see the importance of plotting data.
tio
This case addresses through a typical classroom scenario how data is presented and the benefits of plotting
data. Compared with displaying basic summary statistics like first-order and second-order moments,
plotting data is almost always equally informative or more so. Though summary statistics are often useful
lu
to characterize a dataset and distinguish among datasets, the exercise of plotting data can reveal some
So
The Case Solution Starts From page 4
,• Understand the importance in data analysis and interpretation of plotting the data
• Demonstrate the applications of plotting the graphs
• Understand mean, standard deviation, and regression coefficients
• Demonstrate the concept of the Anscombe quartet
e
pl
m
Sa
n
tio
lu
So
ASSIGNMENT QUESTIONS
1. For the data presented in AQ Data File, calculate the mean and standard deviation of x1 to x4 and y1 to
y4. What are your observations?
2. Calculate the correlation between Xi and Yi for all four samples. What are your observations?
3. Perform regressions of Yi on Xi for all four samples. What are your observations?
4. Based on your observations for the previous three questions, do you think the relationships between Xi
and Yi are the same in all four samples? How would you validate your conclusion? Do statistical tests
support your conclusion?
5. Now plot the data for each pair of variables i.e. (X1, Y1) and (X2, Y2), (X3, Y3) and (X4, Y4)as scatter
plots. Do you find any contradiction with your previous observations? If yes, how can you reconcile?
The Case Solution Starts From page 4
, ANALYSIS
1. For the data presented in AQ Data File, calculate the mean and standard deviation of x1 to x4
and y1 to y4. What are your observations?
As shown in the table below, the mean for the X variables x1 to x4 is 9 and the standard deviation for each
variable is 3.32. The mean for the Y variables from y1 to y4 is 7.50 for each variable and the standard deviation
is 2.03. We can see that the means and standard deviations are the same for each of the four different datasets.
Variable Mean Standard deviation
x1 9 3.32
x2 9 3.32
x3 9 3.32
x4 9 3.32
y1 7.50 2.03
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y2 7.50 2.03
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y3 7.50 2.03
y4 7.50 2.03
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tio
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So
The Case Solution Starts From page 4
