Warm-up *Finish the Titanic Activity!

Numerical Graphs Graphs to use for Quantitative Data

Section 1.2 Analyzing Numerical Data After this section, you should be able to… DESCRIBE numerical graphs CONSTRUCT & INTERPRET dot plots CONSTRUCT & INTERPRET stem-plots Learning Objectives

Describing a Graph There’s a general strategy for interpreting graphs of quantitative data. Look for the overall pattern and for striking departures from that pattern.

Describing a Graph – Numerical Graphs Only!!!!! Overall Pattern Described by: a) Shape b) Center c) Spread Departure Described by: Outlier Outlier – An individual value that falls outside the overall pattern. Don’t forget your SOCS!

Center If you had to pick a single number to describe all the data – the center would be the best. It’s in the middle!

Shape Description Concentrate on Main Features:  Look for Major Peaks – not minor ups and downs  Look for clusters and obvious gaps  Look for possible outliers  Look for symmetry or skewness

Shape – Are there modes? Unimodal Bimodal How many bumps are in the graph? – Those are modes.

UNIMODAL – A Distribution that has 1 mode.

Remember – it will not ALWAYS be EXACTLY the same frequencies, but they will be very close.

Symmetric? Can you fold it along a vertical line through the middle and have the edges math pretty closely? If so, then it’s symmetric. Bell-Shaped

Shape –Skewed? It’s skewed to the side of the longer tail. Negatively Skewed or (Skewed left) Positively Skewed or (Skewed right)

For his own safety, which way should he go “skewing?” Left of Course!

Shape – Unusual Features Are there any stragglers, or outliers? Are there any gaps?

Spread – (Variation) How spread out is the data? How spread out is the interquartile range? Is it tightly clustered around the center or spread out? (What is the Range?) (We will learn more about this later……..)

We looked at the base salaries of the CEOs of the 800 largest corporations in Center – Centered around $500,000 Shape – Unimodal, Nearly Symmetric, Some high outliers Spread – Majority are between $100,000 and 1,000,000. But there are a few with salaries between $2,500,000 and $3,000,000

+ 1)Draw a horizontal axis (a number line) and label it with the variable name. 2)Scale the axis from the minimum to the maximum value. 3)Mark a dot above the location on the horizontal axis corresponding to each data value. Displaying Quantitative Data Dotplots One of the simplest graphs to construct and interpret is adotplot. Each data value is shown as a dot above its location on a number line. How to Make a Dotplot Number of Goals Scored Per Game by the 2004 US Women’s Soccer Team

EPA Estimate of Hwy Gas Mileage (mpg) for midsize cars. Describe the shape, center, and spread of the distribution.

-There are 3 clusters of values: cars that get 25 mpg, 28 – 30 mpg, and 33 mpg. -Large Gaps between 22 mpg, 18 mpg, and 14 mpg. -The center is about 28 mpg. (A typical 2009 model gets 28 mpg) -Spread: Highest value is 33 mpg. Lowest value is 14 mpg. Range = 19 mpg. -Outliers: There are 2 cars with unusually low gas mileage ratings. These cars are possible outliers.

Dotplots How many keys are on your keychain?

Dotplots – You Try one! The following data give the number of hurricanes that happened each year from 1944 through , 2, 1, 2, 4, 3, 7, 2, 3, 3, 2, 5, 2

+ Displaying Quantitative Data Stemplots (Stem-and-Leaf Plots) These data represent the responses of 20 female APStatistics students to the question, “How many pairs ofshoes do you have?” Construct a stemplot Stems Add leaves Order leaves Add a key Key: 4|9 represents a female student who reported having 49 pairs of shoes.

Stemplot – (Stem & Leaf) – Let’s find our pulse rates.

What’s your height? Compare. MaleFemale

Sometimes we have to truncate the data

Grade Point Average

How Long is a Minute

Make & Describe a Stemplot

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