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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

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?

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

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 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 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

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 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 Chart of the Eye Color Data

- 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

- 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

- 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: Average Price for Regular Unleaded Gasoline (Bureau of Labor Statistics)

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.

Average Unemployment Rate Blue = High School GradsPink = College Grads

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.

- 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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