Chapter 12

# Chapter 12 - Chapter 12 Describing Distributions With...

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Chapter 12 Describing Distributions With Numbers

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Outline Median and Quartiles The 5 Number summary Min, Q1, M, Q3, Max Box Plots Mean and Standard Deviation Choosing Numerical Descriptions Measures of Center Measures of Spread
Motivation Investing Money You have \$1000 to invest for 1 year Wal Mart stock prices increased by an average of 2% each year over the last 5 years Nabisco stock prices increased by an average of 3% each year over the last 5 years Who do you invest in?

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More information Year Wal Mart Nabisco 2002 2.2% 10.0% 2003 2.4% -2.0% 2004 1.2% 6.0% 2005 1.8% 4.0% 2006 2.0% -3.0% Average 2.0% 3.0% In light of the new information, would you invest in Wal Mart or Nabisco? Why?
Medians And Quartiles

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Definition The median is the midpoint of a distribution. Half of the observations are smaller than the median and half are larger. Used to describe the center of a distribution The first quartile – Q1 is the median of the smaller half of a distribution. 25% or a quarter of all of the observations in a distribution are smaller than it. The third quartile – Q3 is the median of the larger half of a distribution. 75% or 3 quarters of the observations in a distribution are smaller than it. Q1 and Q3 can be used to describe the spread of a distribution
Examples Rent prices of 7 apartments near campus 245 280 320 400 410 420 440 Q1 M Q3 Salaries of 10 employees (in thousands) 19 22 24 28 32 33 41 42 56 78 M=(32+33)/2 = 32.5 Hours worked in 1 week 14 15 15 17 18 22 26 41 49 50 51 52 Q1 = M = Q3 =

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Calculating Median 1. Sort the data 2. Cross off the outside two numbers one at a time until you are left with one or two numbers. 3. If you have two numbers left, the median is the average of the two numbers. If you have one number left, the median is that number
Example Median Calculation Rent prices data: 320 280 400 440 410 420 245 1. Sort the data: 2. Cross out outside numbers 3. What is the median?

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Salaries of 10 employees (in thousands) 78 32 33 19 41 22 42 56 28 1. Sort the data 19 22 24 28 32 33 41 42 56 78 2. Cross off outside numbers. 3.
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## This note was uploaded on 06/15/2011 for the course STAT 110 taught by Professor Johnson during the Fall '07 term at South Carolina.

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Chapter 12 - Chapter 12 Describing Distributions With...

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