Frequency Distributions and Graphs

Where do we start? Quantitative Data is a set that can be numerically represented.

Dealing With a Lot of Numbers... When looking at large sets of quantitative data, it can be difficult to get a sense of what the numbers are telling us without summarizing the numbers in some way.

What do these data tell us? Make a table –Frequency Distribution Make a picture –Histogram –Stem-and-Leaf Display Describe the distribution –Shape, center, spread, outliers

Frequency Distribution Chart or table with 3 required columns: 1.Classes (# given) Width = 2.Frequency 3.Cumulative Frequency

Example The data shown (in millions of dollars) are the values of the 30 NFL franchises. What can you tell me about this data by looking at the raw data?

Frequency Distribution (8 Classes) Start by sorting the data Class width = (max – min)/(# of classes) = (320 – 170) / 8 = 150 / 8 = ≈ 19

Frequency Distribution (8 Classes) NFL Team Values ClassesFrequencyCumulative Frequency 170 – – – – – – –

Histogram NFL Team Values Class BoundariesClassesFrequencyCumulative Frequency – – – – – – – – – – – – – – – To make a histogram add and subtract 0.5 from either end of the classes.

Histogram To make a histogram put boundaries on x-axis and frequencies on y-axis.

Displaying Quantitative Data Stem and Leaf Display –Leaf Contains the last digit of the values Arranged in increasing order away from stem –Stem Contains the rest of the values Arranged in increasing order from top to bottom

Example – Spurs Last 20 scores of regular season games (’05/’06)

Displaying Quantitative Data Back-to-back Stem-and-Leaf Display –Used to compare two variables –Stems in center column –Leafs for one variable – right side –Leafs for other variable – left side –Arrange leafs in increasing order, AWAY FROM STEM!

Example – Compare Spurs to Pistons Last 20 scores of Pistons regular season games

Looking at Distributions Always report 4 things when describing a distribution: 1.Shape 2.Center 3.Spread 4.Outliers

Looking at Distributions Shape –How many humps (called modes)? None = uniform One = unimodal Two = bimodal Three or more = multimodal

Looking at Distributions Shape –Is it symmetric? Symmetric = roughly equal on both sides Skewed = more values on one side –Right = Tail stretches to large values –Left = Tail stretches to small values

Looking at Distributions Center –A single number to describe the data –Can calculate different numbers for center –For this chapter, just EYE BALL IT – we will learn numerical descriptions next chapter

Looking at Distributions Spread –Variation in the data values Crude measure: Range = max. value – min. value Again, next chapter spread will be a single number Outliers? –Interesting observations in data Can impact statistical methods

65 & Over Histogram 2000 Census Pop Over 65 Frequency

Displaying Categorical Data

Categorical Data Categorical variables are variables that cannot be measured numerically –Examples Gender Religion Colors Race Occupation Emotions

Describing Categorical Data Pie Charts Bar Charts

Pie Chart Displays percentage of whole (for each category) Must include all possible categories

Example of Pie Chart 2004 Enrollment Iowa State University –Agriculture 12% –Business 17% –Design 8% –Education 7% –Engineering 22% –F&C Sciences 6% –Liberal Arts 28%

Bar Charts Displays either number or percentage for each category Do not need to include all possible categories

Example of a Bar Chart Number of students from Iowa and beyond –Iowa: –Non-Iowa U.S.: 4157 –Foreign: 741