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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
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


Roadmap
Roadmap

  • 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

operations: adding, averaging, etc.

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 Graphshttp://blogs.oracle.com/experience/entry/countdown_of_top_10_reasons_to_never_ever_use_a_pie_chart

  • 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


Relative frequency bar graph
Relative Frequency Bar Graphhttp://blogs.oracle.com/experience/entry/countdown_of_top_10_reasons_to_never_ever_use_a_pie_chart


Frequency bar graph
Frequency Bar Graph http://blogs.oracle.com/experience/entry/countdown_of_top_10_reasons_to_never_ever_use_a_pie_chart



Pictogram a Relative Frequency Bar Chart?

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


Be careful about pictogram a Relative Frequency Bar Chart?

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
Line Graph (Bureau of Labor Statistics)

  • 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.


Average unemployment rate blue high school grads pink college grads
Average Unemployment Rate (Bureau of Labor Statistics)Blue = High School GradsPink = College Grads


What should we look for
What should we look for? (Bureau of Labor Statistics)

  • 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 (Bureau of Labor Statistics)

  • 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.


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