Calculating Descriptive Statistics for Student Data

The assignment requires students to calculate descriptive statistics for the variable 'Height' by 'Gender' using a pivot table in Excel. Students are then asked to compare the mean heights of males and females, as well as the standard deviations of their heights. The results are interpreted to conclude that females are shorter than males on average and that male heights are more scattered than female heights.

MATH399 Statistics—Lab Week 2
Question 1 is worth 5 points and each question after that is worth 4.5 points, for a
total of 50 points for the lab.
Name: _______________________
Statistical Concepts:
 Using Excel
 Graphics
 Shapes of distributions
 Descriptive statistics
NOTE: Directions for all labs are given based on Excel 2013 for Windows. If you have
another version of Excel, you may need to research how to do the same steps.
Data in Excel Excel is a powerful, yet user-friendly, data analysis software package. You can
launch Excel by finding the icon and double clicking on it. There are detailed
instructions on how to obtain the graphs and statistics you need for this lab in each
question. There is also a link to an Excel how to document on the iLab page where
you opened this file. Further, if you need more explanation of the Excel functions you
can do an internet search on the function like “Excel standard deviation” or “Excel
pivot table” for a variety of directions and video demonstrations.
 Data have already been formatted and entered into an Excel worksheet. You will see
the link on the page with this lab document. The names of each variable from the
survey are in the first row of the worksheet. All other rows of the worksheet represent
certain students’ answers to the survey questions. Therefore, the rows are called
observations and the columns are called variables. Below, you will find a code sheet
that identifies the correspondence between the variable names and the survey
questions.
Survey Code Sheet: Do NOT answer these questions. The code sheet just lists the
variables name and the question used by the researchers on the survey instrument that
produced the data that are included in the Excel data file. This is just information. The
first question for the lab is after the code sheet.
Variable Name Question
Drive Question 1: How long does it take you to drive to the school on
average (to the nearest minute)?
State Question 2: In what state/country were you born?
Shoe Question 3: What is your shoe size?
Height Question 4: What is your height to the nearest inch?
Sleep Question 5: How many hours did you sleep last night?
Gender Question 6: What is your gender?
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Car Question 7: What color of car do you drive?
TV Question 8: How long (on average) do you spend a day watching
TV?
Money Question 9: How much money do you have with you right now?
Coin Question 10: Flip a coin 10 times. How many times did you get
tails?
Frequency Distributions
1. Create a frequency table for the variable State. In the Excel file, you can click on
Data and then Sort and choose State as the variable on which to sort. Once sorted,
you can count how many students are from each state. From that table, use a
calculator to determine the relative percentages, as well as the cumulative
percentages.
In the box below, type the states from the database in a column to the left, then type
the counts, and relative and cumulative frequencies to the right of the respective state.
Using the data in the table, make a statement about what the frequency counts or
percentages tell about the data.
Table 1: The frequency distribution table of State
The “IL”, “MI” and “SC” states have maximum frequencies (4). These states each
have relative frequencies 11.429%. Many of the students were born in these states.
“GA”, “KY” and “OH” states have least counts (1). These states each have relative
frequencies 2.857%. Very few people were born in those states.
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Creating Graphs
2. Create a bar chart for the frequency table in Question 1. Select the State variable
values. Click on Insert and then click on the arrow on the bottom right of the Charts
area and select Clustered Column and click OK. (Again, different versions of Excel
may need different directions.) Add an appropriate title and axis label. Copy and
paste the graph here.
Figure 1: Frequency Distribution of Staes
CA FL GA IL KY MI NV NY OH OR PA SC TX
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Frequency Distribution of States
States
Frequencies
3. Create a pie chart for the variable Car. Select the column with the Car variable,
including the title of Car. Click on Insert, and then Recommended Charts. It should
show a clustered column and click OK. Once the chart is shown, right click on the
chart (main area) and select Change Chart Type. Select Pie and OK. Click on the pie
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slices, right click Add Data Labels, and select Add Data Callouts. Add an appropriate
title. Copy and paste the chart here.
Figure 2: Frequency distribution of Car Color
black
17%
blue
17%
dark blue
3%
green
9%
orange
6%
red
14%
silver
31%
white
3%
Percentages of Car Color
4. Create a histogram for the variable Height. Use the strategies in the text to create a
frequency table of the heights using the categories of 60–64, 65–69, 70–74, and 75–
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79. It may be helpful to sort the data based on the Height variable first. Create a new
worksheet in Excel by clicking on the + along the bottom of the screen and type in the
categories and the frequency for each category. Then, select the frequency table, click
on Insert, then Recommended Charts and choose the column chart shown and click
OK. Right-click on one of the bars and select Format Data Series. In the pop up box,
change the Gap Width to 0. Add an appropriate title and axis label. Copy and paste
the graph here.
Figure 3: Histogram of Heights
60-64 65-69 70-74 75-79
0
2
4
6
8
10
12
14
16
18
Histogram of Heights
Classes of Heights
Counts
5. Create a stem and leaf chart for the variable Money, using only the whole dollar
amounts. This must be done by hand, as Excel cannot do this type of chart. Using the
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tens value as the stem and the ones value for the leaves, type a stem and leaf plot into
the box below. It may be helpful to sort the data based on the Money variable first.
Figure 4: Stem and Leaf disgram of Money
Stem Leaf
0 1 3 4 5 5 5 5 7 7 7 7 9 9
1 0 3 4 5 6 8
2 0 1 2 3 5 7 8
3 0 4 8
4 3 6 7
5 3 4 4
Calculating Descriptive Statistics
6. Calculate descriptive statistics for the variable Height by Gender. Click on Insert and
then Pivot Table. Click in the top box and select all the data (including labels) from
Height through Gender. Also click on new worksheet and then OK. On the right of
the new sheet, click on Height and Gender, making sure that Gender is in the Rows
box and Height is in the Values box. Click on the down arrow next to Height in the
Values box and select Value Field Settings. In the pop up box, click Average, then
OK. Type in the averages below. Then, click on the down arrow next to Height in the
Values box again and select Value Field Settings. In the pop up box, click on StdDev
then OK. Type the standard deviations below.
Mean Standard Deviation
Females 66.47368421 2.568363531
Males 67.375 4.924428901
 Select File > Save Worksheet As to save the data set. You must either keep a copy of
this data or download it again off the website for future labs.
Short Answer Writing Assignment
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All answers should be complete sentences.
7. What is the most common color of car for students who participated in this survey?
Explain how you arrived at your answer.
The most common color of car for students who participated in this survey is Silver.
The Silver car is observed 11 times out of 35 (31%).
8. What is seen in the histogram created for the heights of students in this class (include
the shape)? Explain your answer.
The histogram of the heights of students in the class indicates that most of the students
have a common height of 65 inches to 69 inches. Very little number of students have
height of 75 inches to 79 inches.
The distribution of heights of all the students is positively skewed.
9. What is seen in the stem and leaf plot for the money variable (including the shape)?
Explain your answer.
The Stem and Leaf diagram refers that most of the students has money in the range of
$1 to $9 (13). The chance of having money from the students in the range of $1 to $29
(count=26) is relatively higher than the chance of having money from the students in
the range of $30 to $59 (count=9).
Most of the students has comparatively lower money with them.
10. Compare the mean for the heights of males and the mean for the heights of females in
these data. Compare the values and explain what can be concluded based on the
numbers.
As per the pivot table, the average height of male students is greater than average
height of females (67.375 inches>66.474 inches). Hence, as an overall scenario,
females are shorter in height than males.
11. Compare the standard deviation for the heights of males and the standard deviation
for the heights of females in the class. Compare the values and explain what can be
concluded based on the numbers.
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The standard deviation of heights is greater for males than females (4.92 inches>2.57
inches). Therefore, the heights of males are more scattered than females and conversely
the heights of females are more concentrated than males.
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