StatisticsGraphic 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 AnalysisJust 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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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

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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

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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 Exact details Later

C – Describe the center

Values of central tendency:MeanMedianMode(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 PlotsAlso known as an

ogive (“oh-jive”)Adds onto each

progressive column

Rabbits born in a month

1 2 3 4 5Week

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Rabbits

Commonly confused with bar graphs

Normal Distribution

Normality Plot

Questions????

Graph ExplorationFind five or more different

graphs and identify the type you think it is.