Summarizing and Describing Data – Use Height_Exam data set (11 Questions)
1. Using Minitab to make a histogram (Graph > Histogram) of the variable Height. Copy and
paste the histogram below.
2. How would you describe the shape of the histogram?
3. Based on the shape of the histogram, would you expect the mean and median to be somewhat
similar or quite different?
4. Use Minitab to find the mean and median (Stat > Basic Statistics > Display Descriptive
Statistics and do NOT change any of the default statistics selected) of the variable Height. What
are the mean and median values and do they agree with what you expected in question 3?
5. According to the Empirical Rule (also called the 68-95-99.7 Rule), for bell shaped data we
would expect about 68% of all observations to fall within one standard deviation of the mean;
about 95% to fall within two standard deviations of the mean; and about all (99.7%) to fall
within three standard deviations of the mean. There are a total of 64 height values in the data set.
Using the Standard Deviation (refer back to your Minitab output you produced for question 4)
apply the Empirical Rule to the Height data by completing the table below [For simplicity,
round the mean to nearest whole number and the SD to one decimal place. Also, you may
want to copy/paste the Height data into Excel to sort. This will make counting the values
within the range easier.]:
Replace mean
and SD with
values
68%
95%
99.7%
Compute the
range (lower and
upper values)
from prior
column
The number of
Height values we
would expect to
find in this range
The actual
number of
Height values
that fell in this
range
Mean ± SD
Mean ± 2*SD
Mean ± 3*SD
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6. From question 4, what is the five number summary for the variable Height?
Minimum:
Q1:
Median:
Q3:
Maximum:
7. As this summary relates to the variable Height, what is the interpretation of first and third
quartile?
8. Do well does the Height data comply with these quartiles? That is, of total number of height
values how many would we expect to fall at or below these quartiles compared to how many
actually fell at or below these quartiles?
Quartile
First (Q1)
Third (Q3)
How many we expected
How many we observed
9. Repeat this the histogram for the variable Exam. Copy and paste the histogram below and
describe the shape and relationship between mean and median.
10. Now let’s apply the Empirical Rule to a data set that is not symmetrical. For the Exam data
the mean is 88 with 11 as the standard deviation. Using this information, complete the
following table. [For simplicity, round the mean and SD to one decimal place. Also, you
may want to copy/paste the Exam data into Excel to sort. This will make counting the
values within the range easier.]:
Replace mean
and SD with
values
68%
95%
99.7%
88 ± 11
88 ± 2*11
88 ± 3*11
Compute the range
(lower and upper
values) from prior
column
The number of Height
values we would
expect to find in this
range
68% of 32 =
95% of 32 =
99.7% of 32 =
The actual
number of Height
values that fell in
this range
11. Outliers and side-by-side boxplots. Outliers are "extreme observations" for a set of data, but
how does one determine what is extreme? Boxplots help us in identifying such observations, and
side-by-side boxplots are very useful when we want to display quantitative data across levels of a
categorical variable, e.g. heights by gender. Create the side-by-side boxplots for Height by
Gender. Click Graph > Boxplot > With Groups. Select Heights for the "Graph Variables" and
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Gender for the "Categorical Variables" and click OK. Copy and paste your graph below and
answer the following questions related to the graph.
A. The '*' symbol in the Female boxplot represents an outlier. By placing your mouse
over the this symbol in Minitab you can determine what the outlier value is and the data row in
which it is located. What is the value and data row?
B. How was this observation determined to be an outlier? To do this, read the online
notes for "Finding Outliers Using IQR" and apply this technique to demonstrate why this
observation would be considered an outlier [NOTE: after reading the online notes you can then
place your mouse over the "box" part of the boxplot in Minitab to get the needed data].
C. In comparing the two boxplots, how would you describe the center and spread of the
heights by gender? More specifically, which gender has the greater mean and median height,
and what about spread, specifically the variance and standard deviation?
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