Interactive Presentation

of 29 /29
AP Statistics Exploring Data Describing Quantitative Data with Numbers EdTech 541 Angie Kruzich September 2014

Embed Size (px)

description

EdTech 541 PowerPoint Presentation

Transcript of Interactive Presentation

  • 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.

    Watch your formatting!

  • 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

    https://www.floridaschoolleaders.org/general/content/NEFEC/dafil/lesson2-5.htm

    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