Transcript Chapter 1 Picturing Distributions with Graphs

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.
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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
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Individuals and variables
Categorical variables:
 Pie Charts and bar graphs
Quantitative variables:
 Histograms
Interpreting histograms
Quantitative variables: Stemplots
Time plots
Examining Distributions- Introduction
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Definitions:
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Individuals: the objects described by a set
of data
Variable: any characteristic of an individual
Examples
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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
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Categorical variable: categories, groups
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Quantitative variable: numerical values
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Distribution of a variable: what values it takes
and how often it takes these values
Examples
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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)
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Exploratory data analysis describes the
main feature of data.
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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
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Distribution of categorical variables categories by
relevant count or percent of individuals.
Graphs: bar graph, pie chart
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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
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How to make histograms
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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
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Interpretation: What do we see?
Overall pattern and striking deviations.
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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
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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
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Data: 80, 52, 86, 94, 76, 48, 92, 69, 79, 45
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Step 1. Sort data in increasing order first
Step 2. Decide stem
Step 3. Fill in leaves
Examples and Exercises
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Example 1.7 (P. 16) using Table 1.1 (P. 10)
Example 1.8 (P. 16)
Tips
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1. Rounding
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2. Splitting stems
Quantitative variables: stemplots
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For small data sets, it is quicker to make and
presents more detailed information
You keep data values
Time plots
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It is for variables which are measured at intervals
over time.
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Example 1. The cost of raw materials for a
manufacturing process each month.
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Example 2. The price of a stock at the end of each
day.
Time plots
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To display change over time, make a time plot. Plot
each observation against the time at which it was
measured
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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
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MAC website:(online tutoring available)
www.gsu.edu/~wwwclc/mathlab.htm