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Understanding Measures of Central Tendency and Dispersion in Statistics

This section covers the fundamental concepts of central tendency, specifically the mean, median, and mode. It explains how these measures summarize data sets and provides examples using test scores to illustrate their calculation. Additionally, it introduces key terms such as measures of dispersion, range, and standard deviation, essential for understanding the spread of data. The process of calculating these statistics using datasets is detailed, alongside instructions for using calculators to find standard deviation efficiently.

elvis-mccormick
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Understanding Measures of Central Tendency and Dispersion in Statistics

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  1. Section 7.3 (p. 259)

  2. Vocabulary • List the 3 measures of Central Tendency A) Mean ( ): _________________________ B) Median: ____________________________ C) Mode: _____________________________ Average Middle # # that occurs the most

  3. Vocabulary #’s used to summarize 1) Statistics: ____________________ ____________________________ 2) Measure of Dispersion: _________ ____________________________ 3) Range: ______________________ & compare sets of data Tells us how spread out the data values are Biggest - Smallest

  4. Vocabulary 4) Standard Deviation : _______ : ________________________ n : ___________ Mean Sigma (Standard Deviation) # of terms

  5. EXAMPLE 1 Find measures of central tendency • TEST SCORES TEST SCORES: 42, 72, 81, 95, 98, 58, 77, 75, 52 83, 97, 45, 89, 93, 57, 82, 97, 75 42, 45, 52, 57, 58, 72, 75, 75, 77, 81, 82, 83, 89, 93, 95, 97, 97, 98 76 79 75 & 97 Mean: ________ Median: ________ Mode: ________

  6. EXAMPLE 2 Find Range • TEST SCORES TEST SCORES: 88, 25, 78, 95, 67, 54 70 Range: ________

  7. EXAMPLE 2 Find Standard Deviation • TEST SCORES TEST SCORES: 88, 25, 78, 95, 67, 54 ( 25 – 68) 2 = 1849 ( 54 – 68) 2 = 196 ( 67 – 68) 2 = 1 ( 78 – 68) 2 = 100 ( 88 – 68) 2 = 400 ( 95 – 68)2 = 729 23.36 Standard Deviation: ________

  8. Writing Data Sets as a LIST OF VALUES • The data set gives the scores for the University of Georgia football team over a 12 game season. 49 21 28 10 7 24 21 12 17 35 42 14

  9. Writing Data Sets as a FREQUENCY TABLE

  10. FINDING STANDARD DEVIATION W/ CALCULATORS • GRAPHING • STAT • 1) EDIT • ENTER #’s in L1 • STAT • Rt Arrow – CALC • 1-VAR STAT • ENTER…ENTER

  11. FINDING STANDARD DEVIATION W/ CALCULATORS YELLOW BLUE data 2nd DATA (STAT) ENTER #’s in L1 - 1-VAR 2nd data (stat) DATA Hit ENTER 4 times - Enter #’s (use arrow) - 1-Var Stats - FRQ = 1 (frequency) - DATA – L1 STATVAR - FRQ – ONE - use arrow key to scroll - CALC

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