What is Statistics?

Definition of Statistics

 Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make a decision.

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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 1 Picturing Distributions with Graphs

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.

Example 1.1 (Page 5)

 Exploratory data analysis describes the main feature of data.

  1. Examine each variable 2. Study the relationships among the variables  3. Start with graphs and add some numerical 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).

Pie Chart in Figure 1.1 shows us each material as a part of the whole

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

Example 1.3 (P. 11)

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

Example 1.5 (P. 13)

Example 1.6 (P. 14)

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

Example 1.9 (P.18)

Free tutoring The Math Assistance Complex (MAC) 122 Kell Hall  MAC website:(online tutoring available) www.gsu.edu/~wwwclc/mathlab.htm