Frequency Distributions

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.

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: CATHERINE OLADOYINBO 1 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
Drive
State
Shoe
Height
Sleep
Gender Question
Question 1: How long does it take you to drive to the school on
average (to the nearest minute)?
Question 2: In what state/country were you born?
Question 3: What is your shoe size?
Question 4: What is your height to the nearest inch?
Question 5: How many hours did you sleep last night?
Question 6: What is your gender?
Version 20160511 Car
TV
Money
Coin Question 7: What color of car do you drive?
Question 8: How long (on average) do you spend a day watching
TV?
Question 9: How much money do you have with you right now?
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. 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.
Version 20160511 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
slices, right click Add Data Labels, and select Add Data Callouts. Add an appropriate
title. Copy and paste the chart here. Version 20160511 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–
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. 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
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. Version 20160511 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
Males 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
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. 8. What is seen in the histogram created for the heights of students in this class (include
the shape)? Explain your answer. Version 20160511 9. What is seen in the stem and leaf plot for the money variable (including the shape)?
Explain your answer. 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. 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. Version 20160511

MATH399
Week 4 Lab [StatCrunch]
Name: _______________________
Statistical Concepts: Probability Binomial Probability Distribution
Calculating Binomial Probabilities Open a new StatCrunch worksheet. Click Multimedia Library under Course Home
and check the StatCrunch checkbox before clicking Find. Click on ANY given
chapter for StatCrunch, and then click Open StatCrunch near the top of your screen
INSTEAD of any of the chapter data files. Change var1 to X, and enter 0 through 10 in the column below. Click the Data
button, then from that menu Compute, then Expression, then Build. Scroll down through the function list to dbinom and double click it. Double click the
X in the Column list on the left of the function listing. Arrow over once and type the
number 10, then arrow over one more time and type the number 0.5. Click Okay,
then Compute. You should see a column header with the dbinom function and it parameters (x,n,p). Repeat for p = 0.25 and p = 0.75. In each case, you should be able to simply edit the
previous expression when it pops up in the Expression menu.
Plotting the Binomial Probabilities
1. Create plots for the three binomial distributions above. Change each of the header
labels to “P(X) for p = .5”, “P(X) for p = .25”, and “P(X) for p = .75”, accordingly.
Click the Graph button and choose Scatter Plot. Select X for the X variable and
P(X) for p = .25 for the Y variable, then Compute, and a graph will appear on screen.
Repeat for the other two columns. Right-click each graph and save the image to your
computer. Use the Insert menu in Word to browse for those images and insert them
into the box below. Do this for each graph image. (12 points) Version 20160520 Calculating Descriptive Statistics You will use the same class survey results that were in the Week 2 iLab Assignment.
Find that spreadsheet and copy the entire Coin column into a blank column in
StatCrunch. Be sure to copy the column header from that spreadsheet along with its
data, and then paste it over one of the var-named headers in StatCrunch, such as var5
or var6—if they are still empty.
2. Calculate descriptive statistics for the variable (Coin) where each of the students
flipped a coin 10 times. Click the Stat button, then Summary Stats, Columns.
Select the Coin column name by clicking it once so that it populates the right-hand
field of that panel. In the Statistics section of this control panel, click Mean, then
CTRL-click Std. dev. Click Compute. Enter the data below. (4 points)
Mean:
Standard deviation:
Short Answer Writing Assignment – Both the calculated binomial probabilities and the
descriptive statistics from the class database will be used to answer the following
questions. Round all numeric values to three decimal places.
3. List the probability value for each possibility in the binomial experiment that was
calculated in StatCrunch with the probability of a success being ½. (Complete
sentence not necessary; round your answers to three decimal places) (10 points)
P(x=0)
P(x=1)
P(x=2)
P(x=3)
P(x=4)
P(x=5) P(x=6)
P(x=7)
P(x=8)
P(x=9)
P(x=10) 4. Give the probability for the following based on the StatCrunch calculations with the
probability of a success being ½. The Binomial Calculator function on the Stat button
menu will help you avoid careless arithmetic error that might come by doing the
Version 20160520 following calculations manually. Click Stat, then Calculators, and Binomial. A
graph should appear with input options for n and p. Enter 10 for n, and 0.5 for p.
Click the inequality symbol and select the appropriate version for each input below.
HINT: The Between button at the top of the panel will help you with one of these, but
be careful and think your way through its limitation, and one of these will require a
manual computation of two separate values. (Complete sentence not necessary;
round your answers to three decimal places) (12 points)
P(x≥1)
P(x>1)
P(4<x ≤7) P(x<0)
P(x≤4)
P(x<4 or x≥7) 5. Calculate (by hand) the mean and standard deviation for the binomial distribution
with the probability of a success being ½ and n = 10. Either show work or explain
how your answer was calculated. Use these formulas to do the hand calculations:
Mean = np, Standard Deviation =
(4 points)
npq
Mean = np:
Standard Deviation = : npq 6. Using all four of the properties of a Binomial experiment (see page 201 in the
textbook) explain in a short paragraph of several complete sentences why the Coin
variable from the class survey represents a binomial distribution from a binomial
experiment. (4 points) 7. Compare the mean and standard deviation for the Coin variable (question 2) with
those of the mean and standard deviation for the binomial distribution that was
calculated by hand in question 5. Explain how they are related in a short paragraph of
several complete sentences. (4 points)
Mean from question #2:
Version 20160520 Standard deviation from question #2:
Mean from question #5:
Standard deviation from question #5:
Comparison and explanation: Version 20160520

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