What is Statistics?

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What is Statistics? Definition of Statistics Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make a decision. Branches of Statistics

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Presentation Transcript
What is Statistics?

Definition of Statistics

• Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make a decision.
• Branches of Statistics
• The study of statistics has two major branches – descriptive(exploratory) statistics and inferential statistics.
• Descriptive statistics is the branch of statistics that involves the organization, summarization, and display of data. In this course, from chapter 1 through Chapter 5, they are talking about Descriptive statistics.
• Inferential statistics is the branch of statistics that involves using a sample to draw conclusions about population. A basic tool in the study of inferential statistics is probability. In this course, starting from Chapter 9, they are talking about inferential statistics.
Chapter outline
• Individuals and variables
• Categorical variables:
• Pie Charts and bar graphs
• Quantitative variables:
• Histograms
• Interpreting histograms
• Quantitative variables: Stemplots
• Time plots
Examining Distributions- Introduction
• Definitions:
• Individuals: the objects described by a set of data
• Variable: any characteristic of an individual
Examples
• College student data: every currently enrolled student – date of birth, gender, major, GPA and so on
• Employee data: every employee – age, gender, salary, job type
Variables
• Categorical variable: categories, groups
• Quantitative variable: numerical values
• Distribution of a variable: what values it takes and how often it takes these values
Examples
• College student data: every currently enrolled student – DOB, gender, major, GPA, and so on
• Employee data: every employee – age, gender, salary, job type
• We can see distributions easily using graphs. It is possible to see distributions using numbers which describe the data.
• 1. Examine each variable
• 2. Study the relationships among the variables

summeries.

Categorical variables--- bar graphs and pie charts
• Distribution of categorical variables categories by relevant count or percent of individuals.
• Graphs: bar graph, pie chart
• Pie chart: figure 1.1 (P. 7)/ must include all categories
• Bar graph: figure 1.2 (P. 8)/heightindividual’s weight

[gaps between bars and order is not important.]

• Note: It’s only for single variable now (for example: college major, tire model, final exam grade).
Quantitative variables: histograms
• How to make histograms
• Step 1. Choose the classes. Divide the range of the data into classes of equal width.
• Step 2. Count the individuals in each class.
• Step 3. Draw the histogram.
• Example 1.3
Interpreting histograms
• Interpretation: What do we see?

Overall pattern and striking deviations.

• Overall pattern

Shape, center, spread: symmetric, skewed to the right/left, clustered.

• striking deviations

Outlier

Quantitative variables: stemplots
• Another way to display a distribution of quantitative variables.
• How to make stemplots
• 1. Sort data in increasing order first
• 2. Separate each observation into a stem consisting of all but the final digit, and a leaf, the final digit.
• 3. Write the stems in a vertical column with the smallest at the top, and draw a vertical line at the right of this column
• 4. Write each leaf in the row to the right of its stem, in increasing order out from the stem.
Quantitative variables: stemplots
• Data: 80, 52, 86, 94, 76, 48, 92, 69, 79, 45
• Step 1. Sort data in increasing order first
• Step 2. Decide stem
• Step 3. Fill in leaves
Examples and Exercises
• Example 1.7 (P. 16) using Table 1.1 (P. 10)
• Example 1.8 (P. 16)
Tips
• 1. Rounding
• 2. Splitting stems
Quantitative variables: stemplots
• For small data sets, it is quicker to make and presents more detailed information
• You keep data values
Time plots
• It is for variables which are measured at intervals over time.
• Example 1. The cost of raw materials for a manufacturing process each month.
• Example 2. The price of a stock at the end of each day.
Time plots
• To display change over time, make a time plot. Plot each observation against the time at which it was measured
• 1. Put time on the horizontal scale
• 2. Put the variable on the vertical scale
• 3. Connect the data points by lines
• Special case: time series (for regularly measured variable)
• You can see: 1 )seasonal variation, 2) trend
Free tutoring

The Math Assistance Complex (MAC) 122 Kell Hall

• MAC website:(online tutoring available) www.gsu.edu/~wwwclc/mathlab.htm