StatisticsStatistics

Graphic distributions

What is Statistics?Statistics is a collection of methods

for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

Uses of Statistics“Some students choose it because it is

required, but increasing numbers do so voluntarily because they recognize its value and application to whatsoever field they plan to pursue. Because employers love to see a statistics course on the transcript of a job applicant, you will have an advantage….” Mario F. Triola

Abuses of StatisticsSmall samplesPrecise numbersGuesstimatesDistorted percentagesPartial picturesDeliberate distortion

More AbusesLoaded questionsPictographsBad SamplesPollster PressureMisleading graphs

Example 1 of Misleading Graphs

Example 2 of Misleading Graphs

Exploratory Data Analysis

Just as an explorer crossing unknown lands tells what he sees, we will be describing the data that we find.– Examine each variable – Describe relationship– Begin with a graph

Nature of Data• Quantitative Data – (QUANTITY)

Numbers representing counts or measurements– EX:

• Qualitative or Categorical Data – (QUALITY) Separated into different categories that can be divided into non-numeric characteristics – EX:

M&M ExperimentMethod of collecting data:

Weigh candies using a digitized scale, check color, and record.

Weights in grams of a sample of M&M candies

.887 .923 .906 .923 .848 .911

.931 .783 .978 .942 .875 .930

.908 .942 .868 .922 .882 .949

.785 .898 .920 .923 .921 .959

.882 .942 .912 .975 .920

.791 .902 .892 .922

Weights in grams of a sample of M&M candies

.887 .923 .906 .923 .848 .911

.931 .783 .978 .942 .875 .930

.908 .942 .868 .922 .882 .949

.785 .898 .920 .923 .921 .959

.882 .942 .912 .975 .920

.791 .902 .892 .922

• What variables are recorded here?• What type of variables are they?

Data

Categorical

Binary

Quantitative

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1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

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1st Qtr 2nd

Qtr

3rd Qtr 4th Qtr

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0% 50% 100%

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr

Types of Graphic Representations

• Frequency distribution• Bar Graph• Stacked Bar Graph

• Pie Charts• Dot Plots• Histograms• Stem and Leaf Plot• …

• Box and Whisker• Time Plot • Scatter Plot

• Cumulative Plots• Normality Plot• Normal Distribution

Frequency Distribution• Pattern of variation• The distribution tells what values a

variable takes and how often• Raw Data

Frequency Distribution List of categories along with counts

Colors in a bag of skittles

Red 14

Yellow 21

Blue 15

Green 21

Purple 17

Orange 15

Bar Graph

• Use of Categorical data

• Attractive• Heights show

counts• More flexible

than pie charts• Vertical and

Horizontal

• Can distort values

Methods of Travel

0

5

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30

35

Boats Cars Planes Trains

Number inthousands

BAR GRAPH EXAMPLE

Stacked Bar Graph• Used to distinguish two or more

categories of the same variable• Great for comparing/ contrasting

two variables

• Can be a little difficult to distinguish size

Number of Toys Purchased

0

50

100

150

200

Board Games

BikesSports Equipment

Game cube

Adults

Girls

Boys

Pie Charts

• Visual • Attractive• Uses categorical data• Easy to interpret

• Difficult to make precise• Must use percents• Close values difficult to

differentiate

Flavors of Ice Cream

Vanilla Chocolate Strawberry Others

PIE CHART EXAMPLE

Guess what percentages these slices represent…

Flavors of Ice Cream

Vanilla Chocolate Strawberry Others

PIE CHART EXAMPLE

Were you close?

Dot Plots• Good Visual • Quantitative data• Check for overall pattern

• Difficult with large amounts of data

Theme Park Attendance Per Day

35 40 45 50 55 60 65 70 75 80 85 90 95 100

105

East Coast Resorts per thousand

West Coast Resorts per thousand

DOT PLOT EXAMPLE

Tools for Interpretation

• Don’t Forget your socks –SOCS

• S – Shape• O –Check for outliers• C – Describe the center• S – Describe the spread

S – Shape• Symmetric?• Skewed to the left?• Skewed to the right ?• Bimodal?

O –Check for outliers

• Stuff that is outside of the normal range

• Details Later

C – Describe the center

Values of central tendency:–Mean–Median–Mode– (Range)

S – Describe the spread

–Wide spread?–Narrow Spread?

–Uniform?

–IQR–Range–Standard Deviation

Stem and Leaf Plot• Sometimes data is too spread out to make a

reasonable dot plot• Five stems is a good minimum• More flexible by rounding• Easy to construct

• Hard with large data sets

Home Run Hits comparison

• Barry Hank• Bonds vs. Aaron • 9 6 1 3• 5 5 4 2 0 4 6 7 9• 7 7 4 4 3 3 3 0 2 4 4 8 9 9• 9 6 2 0 4 0 0 4 4 4 4 5 7• 5• 6• 3 7 17 = 17 hits

Histogram• Quantitative variables• Divides data into classes of equal

size

• Visual may distort understanding

HISTOGRAM EXAMPLE

Box and Whisker Plots• Easy to

compare quartiles

• Outliers seen on modified boxplot

• Side by side = best comparison

• Difficult to determine size of data

• Can be misleading

• Show less detail

Weights of children to age 10

Time Plot• Variables observed

over time• Horizontal axis has

the time scale• Check for overall

pattern

• Does not show what happens WITHIN that time period!

Number of blankets sold each year

Scatter Plot• Shows relationship of two

variables• Can determine overall tendencies• Can determine strength of

relationship

• Not all relationships are linear

Wife’s Age VS Husband’s Age

Cumulative Plots• Also known as an

ogive (“oh-jive”)• Adds onto each

progressive column

Rabbits born in a month

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Rabbits

1 2 3 4 5Week

Commonly confused with bar graphs

Normal Distribution

Normality Plot

Questions????

• The end!!!