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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?
slide3

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%

slide4

Data Tables

  • What makes a good data table?
  • - labels
  • - units
  • - source
  • Tables typically summarize data.
  • But do they tell the whole story?
slide5

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

slide6

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

slide7

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

slide8

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

slide9

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

slide10

Pie Charts

Pie Chart of the Eye Color Data

slide11

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
slide15

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

slide16

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
slide19
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
slide20

Pictogram

  • Typically more interesting than a bar graph because it uses pictures in place of the bars.
slide21

Be careful about pictogram

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
  • 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
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.
slide26

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.
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