STAT 200 Measures of Central Tendency and Dispersion Statistics Worksheet
University of Maryland Global Campus
STAT200 – Assignment #1: Descriptive Statistics Data Analysis Plan
Student (Full Name):
Remove all red-text instructions from this template prior to submission. Save the file as a word document or pdf with the title “LAST_NAME – Assignment 1” (do not submit a rtf file).
Scenario: Please write a few lines describing your scenario and the four variables (in addition to income) you have selected.
Use Table 1 to report the variables selected for this assignment. Note: The information for the required variable, “Income,” has already been completed and can be used as a guide for completing information on the remaining variables. In the subsequent section, explain why you selected each variable as well as the expected outcome.
Table 1. Variables Selected for the Analysis
|Variable Name in the Data Set||Description
(See the data dictionary for describing the variables.)
|Type of Variable
(Qualitative or Quantitative)
|Variable 1: “Income”
|Annual household income in USD.||Quantitative|
Reason(s) for Selecting the Variables and Expected Outcome(s):
- Variable 1: “Income” –
- Variable 2: “ “ –
- Variable 3: “ “ –
- Variable 4: “ “ –
- Variable 5: “ “ –
Proposed Data Analysis:
Measures of Central Tendency and Dispersion
CompleteTable 2. Numerical Summaries of the Selected Variables and briefly explain why you choose those measurements. Note: The information for the required variable, “Income,” has already been completed and can be used as a guide for completing information on the remaining variables.
Table 2. Numerical Summaries of the Selected Variables
|Variable Name||Measures of Central Tendency and Dispersion||Rationale for Why Appropriate|
● Sample Standard Deviation
|I am using median for two reasons:
1. If there are any outliers or the data is not normally distributed, the median is the best measure of central tendency.
2. The variable is quantitative.
I am using sample standard deviation for three reasons:
1. The data is a sample from a larger data set.
2. It is the most commonly used measure of dispersion.
3. The variable is quantitative.
Graphs and/or Tables
Complete Table 3. Type of Graphs and/or Table for Selected Variables and briefly explain why you choose those graphs and/or tables. Note: The information for the required variable, “Income,” has already been completed and can be used as a guide for completing information on the remaining variables. Note: Do NOT simply copy this for the remaining quantitative variables. Make a logical selection based on the data type.
Table 3. Type of Graphs and/or Tables for Selected Variables
|Variable Name||Graph and/or Table||Rationale for why Appropriate?|
|Graph: Histogram||A histogram is one of the best plots available to visually depict the distribution of quantitative level data.|
STAT200 Introduction to Statistics
Dataset for Written Assignments
Description of Dataset:
The data is a random sample from the US Department of Labor’s 2016 Consumer Expenditure Surveys (CE) and provides information about the composition of households and their annual expenditures (https://www.bls.gov/cex/). It contains information from 31 households, where a survey responder provided the requested information; it is all self-reported information. This dataset contains four socioeconomic variables (whose names start with SE) and four expenditure variables (whose names start with USD).
Description of Variables/Data Dictionary:
The following table is a data dictionary that describes the variables and their locations in this dataset (Note: Dataset is on second page of this document):
|Variable Name||Location in Dataset||Variable Description||Coding|
|UniqueID#||First Column||Unique number used to identify each survey responder||Each responder has a unique number from 1-30|
|SE-MaritalStatus||Second Column||Marital Status of Head of Household||Not Married/Married|
|SE-Income||Third Column||Annual Household Income||Amount in US Dollars|
|SE-AgeHeadHousehold||Fourth Column||Age of the Head of Household||Age in Years|
|SE-FamilySize||Fifth Column||Total Number of People in Family (Both Adults and Children)||Number of People in Family|
|USD-AnnualExpenditures||Sixth Column||Total Amount of Annual Expenditures||Amount in US Dollars|
|USD-Food||Seventh Column||Total Amount of Annual Expenditure on Food||Amount in US Dollars|
|USD-Housing||Eighth Column||Total Amount of Annual Expenditure on Housing||Amount in US Dollars|
|USD-Transport||Ninth Column||Total Amount of Annual Expenditure on Transportation||Amount in US Dollars|
How to read the data set: Each row contains information from one household. For instance, the first row of the dataset starting on the next page shows us that for the first household in the sample: the head of household is not married and is 35 years old, has an annual household income is $97,469, has a family size of 4, annual expenditures of $54,929, and spends $6,900 on food, $18,514 on housing, and $145 on transportation.
STAT200 Introduction to Statistics
Assignment #1: Descriptive Statistics Data Analysis Plan
Assignment #1: Prepare Descriptive Statistics Data Analysis Plan
Before conducting any statistical analyses, researchers develop a plan for how they will analyze their data to answer their research questions. The purpose of this assignment is to provide an experience developing a descriptive statistics analysis plan. Note: This first assignment is a plan only; no statistics will be calculated or graphs created. The second assignment will involve carrying out the plan, after receiving feedback from your instructor.
Step #1: Review the provided STAT200 data set file. (Note: This data set will be used for all three of this term’s written assignments).
The provided data set is a subsample of 31 data points from the US Department of Labor’s Consumer Expenditure Surveys (CE) and provides information about the composition of households and their annual expenditures (https://www.bls.gov/cex/). Detailed information on the sample and variables is included with the data set file; please carefully review this information to familiarize yourself with the data (Note: This information will be used in Assignment #2 to describe the dataset).
Step #2: Develop descriptive statistics data analysis plan.
- Task 1: Develop scenario. Imagine that you are head of a household and have to determine a household budget plan based on the data available from the dataset. For instance, you are a 35 year old single parent with a high school diploma and one child.
The “scenario” you describe is just to explain why you might be motivated to do this analysis. It does NOT have to be correct and/or true. As an example:
*Note that this is an example and that the data variables may not be the same as in our data set. You MUST create the scenario using the variables in our data set.*
“I am a 35 year old married parent (head of household) with one child. I earn $97,000 per year, and I spend $8,200 per year on food (including dining out): $1,800 of it is on meat, $0 on bakery items, and $150 on fruits (I’m on the Keto diet, so I spend more on protein than carbs). I want to determine how my income and expenditures relate to other people in the United States.”
You could also do something like this (but realize that this statement uses variables that are
NOT in our data set):
“I’m a 16-year old medical doctor (child prodigy) who makes $248,000 a year. I have no kids, but I do have some college debt to pay off ($2,648 per month–med school is expensive!). I also
STAT200: Written Assignment #1 – Descriptive Statistics Data Analysis Plan – Instructions Page 1 of 5
have pay for food ($12,400–I eat out a lot), electricity ($6,400–I keep my apartment chilled), and transportation ($600–I don’t have a car yet). I want to learn how my current situation matches up to or differs from other people.”
This statement is probably not true, but it will make me smile while reading it. 🙂 The last statement is important, though. No one analyzes data sets for fun (even I don’t do that), so briefly explain why you are undertaking this process (other than you are told to do it for this class).
(NOTE: You do not need to put your actual income or any expenditure values in here–that is personal information that I do not need to know).
A key point here is to ensure you use variables from the data set that accompany our section.
The variables described above may not actually apply to our section (they are “general” or “generic”).
- Task 2: Select variables for analysis that match the scenario developed in Task 1. The data set provides information on household consumption; there are socioeconomic variables and expenditures variables. The socioeconomic variable names start with “SE-” and the expenditure variable names start with a “USD;” all expenditures are in US dollars. All students must use income as one variable. Select two additional socioeconomic variables (one qualitative and one quantitative) and two expenditures for your analysis that match the scenario you developed for Task 1.
For instance, using the example scenario of a 35 year old single parent with a high school diploma and one child, you could select “income,” “education,” and “number of children” as
socioeconomic variables and then pick two household expenditure items to show the distribution of costs and compare that with your income. For this assignment, though, only select variables that are included with our section’s data set (and income, education, and
number of children may or may not be in our data set; these are just example variables include to aid in understanding).
When selecting variables, think about the following three questions:
o Why am I choosing these variables?
o What interests me about these variables?
o What do I think will be the outcome?
Answer these questions in the section on the template labeled: “Reason(s) for Selecting the
Variables and Expected Outcome(s):”.
STAT200: Written Assignment #1 – Descriptive Statistics Data Analysis Plan – Instructions Page 2 of 5
- Task 3: Determine appropriate measures of central tendency and dispersion for the selected variables. For each quantitative variable, select at least one measure of central tendency and at least one measure of dispersion (Please see table below for list of measures). For the qualitative variable, select one measure of central tendency. When determining the measures of central tendency and dispersion, think about what is appropriate given the level of measurement and type of variable. Recommend referring to the text and information posted in our LEO classroom to help with this task (Note: you will use this information to provide a rationale for your choice of measures)
|Measures of Central Tendency||Measures of Dispersion|
|● Mean||● Range|
|● Mode||● Sample Standard Deviation|
|● Median||● Variance|
- Task 4: Determine appropriate graph and/or table for each of the selected variables. Select one graph or table for each variable (Please see below table for list of graphs and tables). When determining the graphs and tables, think about what is appropriate given the level of measurement and type of variable. Recommend referring to the text and information posted in our LEO classroom to help with this task (Note: you will use this information to provide a rationale for your choice of graphs and/or tables).
|Types of Graphs||Types of Tables|
|● Pie Chart||● Frequency Table|
|● Bar Chart||● Relative Frequency Table|
|● Histogram||● Grouped Frequency Table|
|● Box Plots (also known as Box-and-Whiskers Plot)|
STAT200: Written Assignment #1 – Descriptive Statistics Data Analysis Plan – Instructions Page 3 of 5
Step #3: Complete the “Assignment #1: Descriptive Statistics Data Analysis Plan Template.”
Remember, you will not be conducting any statistical analysis, drawing any graphs, or compiling any tables for the first assignment. Rather, you need to wait for feedback from your instructor on this assignment and use that feedback to complete Assignment #2.
Here are the main sections for this assignment (i.e., completing the plan template):
- Identifying Information. Fill in information on name, class, instructor, and date.
- In this section, briefly (2-3 sentences) describe the scenario you developed in Step #2, Task 1.
- Complete Table 1: Variables Selected for the Analysis. Enter information the variables selected for analysis in Step #2, Task 2. For each selected variable be sure to include its: name as listed in the data set, description, and variable type.
- Reason(s) for Selecting the Variables and Expected Outcome(s): In this section, for each selected variable, please answer the following questions:
- Why did I choose this variable?
- What interests me about this variable?
- What do I think will be the outcome?
- Complete Table 2. Numerical Summaries of the Selected Variables. Enter information on selected measures of central tendency and dispersion for each selected variable. Be sure to briefly explain why you choose those measurements. Note: The information for the required variable, “Income,” has already been completed and can be used as a guide for completing information on the remaining variables.
- Complete Table 3. Type of Graphs and/or Tables for Selected Variables. Enter information on selected graph and/or table for each selected variable. Be sure to briefly explain why you choose those measurements. Note: The information for the required variable, “Income,” has already been completed and can be used as a guide for completing information on the remaining variables.
- Assignment Submission: Save the file that contains your completed “Assignment #1:
Descriptive Statistics Data Analysis Plan Template” as a pdf or docx using the following format: “LastName, First Name – Assignment1.” Then, submit the file via the Assignments area in the LEO classroom in the “Assignment #1: Descriptive Statistics Data Analysis Plan” folder and wait for your instructor’s feedback.
STAT200: Written Assignment #1 – Descriptive Statistics Data Analysis Plan – Instructions Page 4 of 5
Grading Rubric for Written Assignment #1
Your instructor will use this grading rubric when grading your assignment submission:
|Scenario and Selection of Related Variables:|
|● Clear description of scenario||20%|
|● Selected variables and reasons are appropriate for the scenario.|
|Selection of Measures of Central Tendency and Dispersion|
|For each variable:||30%|
|● Appropriate measures selected.|
|● Rationale is provided and appropriate.|
|Selection of Graphs and/or Tables|
|For each variable:||30%|
|● Appropriate measures selected.|
|● Rationale is provided and appropriate.|
|● Completes all sections of template.||20%|
|● Writes clearly, concisely, and with few errors.|
STAT200: Written Assignment #1 – Descriptive Statistics Data Analysis Plan – Instructions Page 5 of 5