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Statistics with Economics and Business Applications
Statistics with Economics and Business Applications
Review
Review
Descriptive and Inferential Statistics
Descriptive and Inferential Statistics
Variables and Data
Variables and Data
Definitions
Definitions
Example
Example
Example
Example
How many variables have you measured
How many variables have you measured
Types of Variables
Types of Variables
Types of Variables
Types of Variables
Types of Variables
Types of Variables
Examples
Examples
Graphing Qualitative Variables
Graphing Qualitative Variables
Example
Example
Graphs
Graphs
Scatterplots
Scatterplots
Stem and Leaf Plots
Stem and Leaf Plots
Example
Example
Interpreting Graphs: Location and Spread
Interpreting Graphs: Location and Spread
Interpreting Graphs: Shapes
Interpreting Graphs: Shapes
Interpreting Graphs: Outliers
Interpreting Graphs: Outliers
Example
Example
Relative Frequency Histograms
Relative Frequency Histograms
How to Draw Relative Frequency Histograms
How to Draw Relative Frequency Histograms
How to Draw Relative Frequency Histograms
How to Draw Relative Frequency Histograms
Example
Example
Age
Age
Describing the Distribution
Describing the Distribution
Key Concepts
Key Concepts
Key Concepts
Key Concepts

Презентация: «Statistics with Economics and Business Applications». Автор: Valued Gateway Client. Файл: «Statistics with Economics and Business Applications.ppt». Размер zip-архива: 748 КБ.

Statistics with Economics and Business Applications

содержание презентации «Statistics with Economics and Business Applications.ppt»
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1 Statistics with Economics and Business Applications

Statistics with Economics and Business Applications

Chapter 2 Describing Sets of Data Descriptive Statistics - Tables and Graphs

2 Review

Review

I. What’s in last lecture? 1. inference process 2. population and samples II. What's in this lecture? Descriptive Statistics – tables and graphs. Read Chapter 2.

3 Descriptive and Inferential Statistics

Descriptive and Inferential Statistics

Statistics can be broken into two basic types: Descriptive Statistics (Chapter 2): Methods for organizing, displaying and describing data by using tables, graphs and summary statistics. Descriptive statistics describe patterns and general trends in a data set. It allows us to get a ``feel'' for the data and access the quality of the data. Inferential Statistics (Chapters 7-13): Methods that making decisions or predictions about a population based on sampled data.

4 Variables and Data

Variables and Data

A variable is a characteristic that changes or varies over time and/or for different individuals or objects under consideration. Examples: Hair color, white blood cell count, time to failure of a computer component.

5 Definitions

Definitions

An experimental unit is the individual or object on which a variable is measured. A measurement results when a variable is actually measured on an experimental unit. A set of measurements, called data, can be either a sample or a population.

6 Example

Example

Variable Hair color Experimental unit Person Typical Measurements Brown, black, blonde, etc.

7 Example

Example

Variable Time until a light bulb burns out Experimental unit Light bulb Typical Measurements 1500 hours, 1535.5 hours, etc.

8 How many variables have you measured

How many variables have you measured

Univariate data: One variable is measured on a single experimental unit. Bivariate data: Two variables are measured on a single experimental unit. Multivariate data: More than two variables are measured on a single experimental unit.

9 Types of Variables

Types of Variables

10 Types of Variables

Types of Variables

Qualitative variables measure a quality or characteristic on each experimental unit. Examples: Hair color (black, brown, blonde…) Make of car (Dodge, Honda, Ford…) Gender (male, female) State of birth (California, Arizona,….)

11 Types of Variables

Types of Variables

Quantitative variables measure a numerical quantity on each experimental unit. Discrete if it can assume only a finite or countable number of values. Continuous if it can assume the infinitely many values corresponding to the points on a line interval.

12 Examples

Examples

For each orange tree in a grove, the number of oranges is measured. Quantitative discrete For a particular day, the number of cars entering a college campus is measured. Quantitative discrete Time until a light bulb burns out Quantitative continuous

13 Graphing Qualitative Variables

Graphing Qualitative Variables

Use a data distribution to describe: What values of the variable have been measured How often each value has occurred “How often” can be measured 3 ways: Frequency Relative frequency = Frequency/n Percent = 100 x Relative frequency

14 Example

Example

A bag of M&M®s contains 25 candies: Raw Data: Statistical Table:

Color

Tally

Frequency

Relative Frequency

Percent

Red

5

5/25 = .20

20%

Blue

3

3/25 = .12

12%

Green

2

2/25 = .08

8%

Orange

3

3/25 = .12

12%

Brown

8

8/25 = .32

32%

Yellow

4

4/25 = .16

16%

15 Graphs

Graphs

Bar Chart

Pie Chart

16 Scatterplots

Scatterplots

The simplest graph for quantitative data Plots the measurements as points on a horizontal axis, stacking the points that duplicate existing points. Example: The set 4, 5, 5, 7, 6

17 Stem and Leaf Plots

Stem and Leaf Plots

A simple graph for quantitative data Uses the actual numerical values of each data point.

Divide each measurement into two parts: the stem and the leaf. List the stems in a column, with a vertical line to their right. For each measurement, record the leaf portion in the same row as its matching stem. Order the leaves from lowest to highest in each stem.

18 Example

Example

The prices ($) of 18 brands of walking shoes: 90 70 70 70 75 70 65 68 60 74 70 95 75 70 68 65 40 65

19 Interpreting Graphs: Location and Spread

Interpreting Graphs: Location and Spread

Where is the data centered on the horizontal axis, and how does it spread out from the center?

20 Interpreting Graphs: Shapes

Interpreting Graphs: Shapes

21 Interpreting Graphs: Outliers

Interpreting Graphs: Outliers

Are there any strange or unusual measurements that stand out in the data set?

22 Example

Example

A quality control process measures the diameter of a gear being made by a machine (cm). The technician records 15 diameters, but inadvertently makes a typing mistake on the second entry.

1.991 1.891 1.991 1.988 1.993 1.989 1.990 1.988 1.988 1.993 1.991 1.989 1.989 1.993 1.990 1.994

23 Relative Frequency Histograms

Relative Frequency Histograms

A relative frequency histogram for a quantitative data set is a bar graph in which the height of the bar shows “how often” (measured as a proportion or relative frequency) measurements fall in a particular class or subinterval.

24 How to Draw Relative Frequency Histograms

How to Draw Relative Frequency Histograms

Divide the range of the data into 5-12 subintervals of equal length. Calculate the approximate width of the subinterval as Range/number of subintervals. Round the approximate width up to a convenient value. Use the method of left inclusion, including the left endpoint, but not the right in your tally. (Different from the guideline in the book). Create a statistical table including the subintervals, their frequencies and relative frequencies.

25 How to Draw Relative Frequency Histograms

How to Draw Relative Frequency Histograms

Draw the relative frequency histogram, plotting the subintervals on the horizontal axis and the relative frequencies on the vertical axis. The height of the bar represents The proportion of measurements falling in that class or subinterval. The probability that a single measurement, drawn at random from the set, will belong to that class or subinterval.

26 Example

Example

The ages of 50 tenured faculty at a state university. 34 48 70 63 52 52 35 50 37 43 53 43 52 44 42 31 36 48 43 26 58 62 49 34 48 53 39 45 34 59 34 66 40 59 36 41 35 36 62 34 38 28 43 50 30 43 32 44 58 53

We choose to use 6 intervals. Minimum class width = (70 – 26)/6 = 7.33 Convenient class width = 8 Use 6 classes of length 8, starting at 25.

27 Age

Age

Tally

Frequency

Relative Frequency

Percent

25 to < 33

1111

5

5/50 = .10

10%

33 to < 41

1111 1111 1111

14

14/50 = .28

28%

41 to < 49

1111 1111 111

13

13/50 = .26

26%

49 to < 57

1111 1111

9

9/50 = .18

18%

57 to < 65

1111 11

7

7/50 = .14

14%

65 to < 73

11

2

2/50 = .04

4%

28 Describing the Distribution

Describing the Distribution

Shape? Outliers? What proportion of the tenured faculty are younger than 41? What is the probability that a randomly selected faculty member is 49 or older?

Skewed right No.

(14 + 5)/50 = 19/50 = .38 (9+ 7 + 2)/50 = 18/50 = .36

29 Key Concepts

Key Concepts

I. How Data Are Generated 1. Experimental units, variables, measurements 2. Samples and populations 3. Univariate, bivariate, and multivariate data II. Types of Variables 1. Qualitative or categorical 2. Quantitative a. Discrete b. Continuous III. Graphs for Univariate Data Distributions 1. Qualitative or categorical data a. Pie charts b. Bar charts

30 Key Concepts

Key Concepts

2. Quantitative data a. Scatterplot b. Stem and leaf plots c. Relative frequency histograms 3. Describing data distributions a. Shapes—symmetric, skewed left, skewed right, unimodal, bimodal b. Proportion of measurements in certain intervals c. Outliers

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