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AP Statistics Exploring Data Describing Quantitative Data with Numbers EdTech 541 Angie Kruzich September 2014
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• AP Statistics Exploring Data Describing Quantitative Data with Numbers

EdTech 541 Angie Kruzich September 2014

• Learning Objectives

MEASURE center using mean & median

CALCULATE mean

DETERMINE median

COMPARE mean & median

CONSTRUCT a boxplot

• Measuring Center: The Mean

The most common measure of center is the ordinary arithmetic average, or mean, , (pronounced x-bar).

x

• Calculate mean by adding all data values and dividing by number of observations.

If the n observations are x1, x2, x3, , xn, then:

x sum of observations

n

x1 x2 ... xnn

Mean Definition

• In mathematics, the capital Greek letter (sigma) is short for add them all up. Therefore, the mean formula can also be written:

x xi

n

More Mean

• Measuring Center: The Median Another common measure of center is

the median. The median describes the midpoint of a distribution.

• Median Definition

It is the midpoint of a distribution such

that half of the observations are smaller and the other half larger.

• Finding Median

1. Arrange numbers from smallest to largest.

2. The Median is the number in the middle, unless

• Odd versus Even Numbers of Data

• Interactive Quiz

Obtain an Nspire classroom calculator

Log on

Your teacher will be sending you a document

• Quiz Measuring Center

Calculate the mean and median of the commuting times (in minutes) of 20 randomly selected New York workers.

10 30 5 25 40 20 10 15 30 20 15 20 85 15 65 15 60 60 40 45

• Quiz Measuring Center

On page 1.1 finish entering the data in the spreadsheet.

Press control right/left

arrow to change pages on calculator.

10 30 5 25 40 20 10 15 30 20 15 20 85 15 65 15 60 60 40 45

• Quiz Measuring Center

Read the instructions on page 1.2.

• Quiz Measuring Center

On page 1.3 use the calculator page provided to calculate the mean.

• Quiz Measuring Center

On page 1.4 and 1.5 enter your final solutions.

Press control arrow up when you are done.

• 0 5

1 005555

2 0005

3 00

4 005

5

6 005

7

8 5

Key: 4|5

represents a

New York

worker who

reported a 45-

minute travel

time to work.

M 20 25

2 22.5 minutes

Quiz Median Solution

To calculate the median:

10 30 5 25 40 20 10 15 30 20 15 20 85 15 65 15 60 60 40 45

• Quiz Mean Solution

To calculate the mean:

x 10 30 5 25 ... 40 45

20 31.25 minutes

10 30 5 25 40 20 10 15 30 20 15 20 85 15 65 15 60 60 40 45

• If mean and median are close together, then distribution is roughly symmetric.

If mean and median are exactly the same, distribution is exactly symmetric.

Comparing the Mean and the Median

• In a skewed distribution, the mean is usually farther out in the long tail than is the median.

Comparing the Mean and the Median

• The mean and median measure center in different ways.

Dont confuse the average value of a variable with its typical value.

Comparing the Mean and the Median

• The Five Number Summary

The mean and median tell us little about the tails of a distribution.

The five-number summary of a distribution consists of:

• What are Quartiles?

• Constructing Boxplots Also known as box-and-whisker plots. The five number summary gives us values to

construct a boxplot: Minimum Q1 M Q3 Maximum

• Constructing Boxplots

• Consider our NY travel times data. In your groups, discuss & construct a

boxplot for the data on your Nspires.

Constructing Boxplots

10 30 5 25 40 20 10 15 30 20 15 20 85 15 65 15 60 60 40 45

• M = 22.5 Q3= 42.5 Q1 = 15 Min=5

10 30 5 25 40 20 10 15 30 20 15 20 85 15 65 15 60 60 40 45

5 10 10 15 15 15 15 20 20 20 25 30 30 40 40 45 60 60 65 85

Max=85

Constructing Boxplots

• Summary

Mean is average

Median is middle

How to compare mean and median

How to construct a boxplot

• Resources Images Slide 3 Courtesy of Math is Fun

http://www.mathsisfun.com/definitions/mean.html

Slide 6 Courtesy of W3.org

http://www.w3.org/2013/11/w3c-highlights/

Slide 7 Courtesy of Knowledge Center

http://knowledgecenter.csg.org/kc/content/stats-101-mean-versus-median

Slide 8 Courtesy of Sparkle Box

http://www.sparklebox.co.uk/6771-6780/sb6779.html#.VCigcRaK18E

Slide 10 Courtesy of Underwood Distributing

http://www.underwooddistributing.com/shop/shop?page=shop.browse&category_id=109

Slide 11 Courtesy of Streetsblog USA

http://usa.streetsblog.org/2008/01/10/does-times-square-have-too-many-people-or-just-too-many-cars/

• Images Slide 18 Courtesy of Profit of Education

http://profitofeducation.org/?p=2152

Slide 19 and 20 Courtesy of Data Analysis for Instructional Leaders

Slide 21 Courtesy of Penn State

https://onlinecourses.science.psu.edu/stat100/node/11

Slide 23 and 25 Courtesy of GCSE Math Notes

http://astarmathsandphysics.com/gcse-maths-notes/gcse-maths-notes-five-figure-summaries-and-boxplots.html

Reference Starnes, D., Yates, D., & Moore, D. (2011). The practice of statistics. New York,

New York: W.H. Freeman and Company.

Resources