STAT 110 - Section 5 Lecture 12

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STAT 110 - Section 5 Lecture 12. Professor Hao Wang University of South Carolina Spring 2012. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A. Roadmap. Statistics deals with data. We know how to get good data. - random sampling 

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STAT 110 - Section 5 Lecture 12

Professor Hao Wang

University of South Carolina

Spring 2012

TexPoint fonts used in EMF.

Read the TexPoint manual before you delete this box.: AAAAA

• Statistics deals with data.
• We know how to get good data.
• - random sampling 
• - randomized comparative experiments 
• So, what’s the best way to present data?

Data Tables

Eye Color of 46 Students

Eye Color # of persons percent

Brown 18 39%

Blue 17 37%

Green 6 13%

Hazel 4 9%

Other 1 2%

Total 46 100%

Data Tables

• What makes a good data table?
• - labels
• - units
• - source
• Tables typically summarize data.
• But do they tell the whole story?

Types of Variables

categorical variable – places an individual into one of several groups or categories

Example: Gender, college attended, field of study

quantitative variable – takes numerical values for which arithmetic operations make sense

Example: Height, income, GPA, stock price, length

Eye Color of 46 Students

Eye Color # of persons percent

Brown 18 39%

Blue 17 37%

Green 6 13%

Hazel 4 9%

Other 1 2%

Total 46 100%

What kind of variable is eye color?

A – Categorical

B - Quantitative

Eye Color of 46 Students

Eye Color # of persons percent

1 18 39%

2 17 37%

3 6 13%

4 4 9%

5 1 2%

Total 46 100%

What kind of variable is eye color?

A – Categorical

B - Quantitative

Definitions

frequency – the number of times a value occurs in the data

relative frequency – for a value, the proportion (fraction or percent) of all observations that have that value

Eye Color of 46 Students

Eye Color # of persons percent

Brown 18 39%

Blue 17 37%

Green 6 13%

Hazel 4 9%

Other 1 2%

Total 46 100%

Which column is the frequency?

A – Eye Color

B - # persons

C - percent

Pie Charts

Pie Chart of the Eye Color Data

Pie Charts

• shows how a whole is divided into parts
• How do you make a pie chart?
• (1) draw a circle - this represents the whole
• (2) draw wedges in proportion to the size of each part - each wedge represents each part
• angles are harder to compare than lengths.
• not a good way to compare sizes of the parts

http://blogs.oracle.com/experience/entry/countdown_of_top_10_reasons_to_never_ever_use_a_pie_charthttp://blogs.oracle.com/experience/entry/countdown_of_top_10_reasons_to_never_ever_use_a_pie_chart

http://anametrix.com/index.php/easyblog/entry/pie-charts-are-everywhere-and-they-are-awful

Bar Graphs

• height of each bar shows rate or count
• easier to draw than a pie chart
• Called a “Frequency Bar Graph” when counts are used
• Called a “Relative Frequency Bar Graph” when percentages are used
Which of the values can not be used on the vertical axis of a Relative Frequency Bar Chart?
• A. 0
• B. 0.25
• C. 50%
• D. 150

Pictogram

• Typically more interesting than a bar graph because it uses pictures in place of the bars.

Plus: Can be more visually appealing than a bar graph

Minus: Can be misleading because our eyes respond to total area, not just height

Line Graph
• To display change over time, make a line graph. This can be used to display a quantitative variable changing over time. A line graph of a variable plots each observation against the time at which it was measured.
• Time always goes on the horizontal scale.
• Variable you’re measuring always goes on the vertical scale.
• Connect the data points by lines to display the change over time.
What should we look for?
• Overall pattern.
• A trend is a long-term upward or downward movement over time.
• Striking deviations.
• Seasonal variation.
• A pattern that repeats itself at known regular intervals of time is called seasonal variation.
• Many series of regular measurements over time are seasonally adjusted.

Making Good Graphs

• Use good labels and legends.
• - variables, units, source
• Make the data stand out!
• - Drawing a graph isn’t a creative art project.
• Pay attention to what the eye sees.
• - Avoid pictograms and fancy 3D effects.
• Watch the scales.