# STAT 200 Measures of Central Tendency and Dispersion Statistics Worksheet

STAT 200 Measures of Central Tendency and Dispersion Statistics Worksheet

University of Maryland Global Campus

STAT200 – Assignment #1: Descriptive Statistics Data Analysis Plan

Identifying Information

Student (Full Name):

Class:

Instructor:

Date:

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 Variable 2: Variable 3: Variable 4: Variable 5:

Reason(s) for Selecting the Variables and Expected Outcome(s):

1. Variable 1: “Income” –
2. Variable 2: “ “ –
3. Variable 3: “ “  –
4. Variable 4: “ “  –
5. 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 Variable 1: “Income” ●        Median ●        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. Variable 2: Variable 3: Variable 4: Variable 5:

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? Variable 1: “Income” Graph: Histogram A histogram is one of the best plots available to visually depict the distribution of quantitative level data. Variable 2: Variable 3: Variable 4: Variable 5:

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.

 UniqueID# SE-MaritalStatus SE-Income SE-AgeHeadHousehold SE-FamilySize USD-AnnualExpenditures USD-Food USD-Housing USD-Transport 1 Not Married 97469 35 4 54929 6900 18514 145 2 Not Married 97912 49 1 55704 6937 18619 152 3 Not Married 96697 49 2 56453 6971 18520 136 4 Not Married 96653 51 4 56488 6943 18838 124 5 Not Married 96664 53 3 55558 7051 18502 168 6 Not Married 95744 52 4 55963 7040 18435 146 7 Not Married 94929 59 2 55247 6948 18483 133 8 Not Married 96928 43 3 55932 6953 18701 145 9 Not Married 97681 53 4 56124 7097 18676 134 10 Not Married 96244 56 4 56051 7073 18484 141 11 Not Married 96886 44 2 55321 6982 18312 153 12 Not Married 96727 39 2 56440 7051 18376 120 13 Not Married 96690 57 2 56097 6822 18334 135 14 Not Married 96572 59 2 56515 7179 18648 123 15 Not Married 98717 40 3 56393 7036 18389 114 16 Married 106292 57 4 82299 10983 23063 132 17 Married 95801 54 3 73798 9395 23155 151 18 Married 95385 50 4 74110 9101 22847 211 19 Married 95865 46 1 74789 9321 22621 168 20 Married 109312 37 6 80801 10564 25392 58 21 Married 114051 42 5 84486 10820 25728 167 22 Married 110651 58 4 83766 11226 22899 113 23 Married 107338 67 2 83651 11710 21893 47 24 Married 101829 45 4 82385 10821 22409 121 25 Married 102244 34 4 74687 8735 27964 60 26 Married 113558 31 5 79861 10346 25006 141 27 Married 100947 35 4 73973 8455 26783 36 28 Married 107369 66 2 83441 11724 23174 82 29 Married 106894 51 5 81585 11360 22396 162 30 Married 97769 47 5 73950 9035 22867 202 31 Married 98885 45 4 57795 9653 23400 152

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.

Assignment Steps:

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 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