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 Statistics Small samples Precise numbers Guesstimates Distorted percentages Partial pictures Deliberate distortion

More Abuses Loaded questions Pictographs Bad Samples Pollster Pressure Misleading 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 Qualitative or Categorical Data – (QUALITY) Separated into different categories that can be divided into non-numeric characteristics

M&M activity Method of collecting data Weigh candies using a digitized scale, check color, and record.

Weights in grams of a sample of M&M candies

Data Categorical Binary CategoricalQuantitative

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 Red14 Yellow21 Blue15 Green21 Purple17 Orange15

Bar Graph Use of Categorical data Attractive Heights show counts More flexible than pie charts Vertical and Horizontal Can distort values

Methods of Travel 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

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 PIE CHART EXAMPLE Guess what percentages these slices represent…

Flavors of Ice Cream 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 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 left skewed 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 –Symmetrical –Skewed –Uniform

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 = 17 hits

Histogram Quantitative variables Divides data into classes equal in 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

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 Week Commonly confused with bar graphs

Normal Distribution

Normality Plot

Questions???? The end!!!