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Unformatted text preview: Chapter 6 – 1 Chapter 6: Sampling and the Normal Distribution • Properties of the Normal Distribution • Shapes of Normal Distributions • Standard (Z) Scores • The Standard Normal Distribution • Transforming Z Scores into Proportions • Transforming Proportions into Z Scores • Finding the Percentile Rank of a Raw Score • Finding the Raw Score for a Percentile Chapter 6 – 2 • Normal Distribution – A bellshaped and symmetrical theoretical distribution , with the mean, the median, and the mode all coinciding at its peak and with frequencies gradually decreasing at both ends of the curve. Normal Distributions • The normal distribution is a theoretical ideal distribution. Reallife empirical distributions never match this model perfectly. However, many things in life do approximate the normal distribution, and are said to be “normally distributed.” Chapter 6 – 3 Scores “Normally Distributed?” • Is this distribution normal? • There are two things to initially examine: (1) look at the shape illustrated by the bar chart, and (2) calculate the mean , median , and mode . Table 10.1 Final Grades in Social Statistics of 1,200 Students (19831993) Midpoint Score Frequency Bar Chart Freq. Cum. Freq. (below) % Cum % (below) 40 * 4 4 0.33 0.33 50 ******* 78 82 6.5 6.83 60 *************** 275 357 22.92 29.75 70 *********************** 483 840 40.25 70 80 *************** 274 1114 22.83 92.83 90 ******* 81 1195 6.75 99.58 100 * 5 1200 0.42 100 Chapter 6 – 4 Scores Normally Distributed! • The Mean = 70.07 • The Median = 70 • The Mode = 70 • Since all three are essentially equal , and this is reflected in the bar graph, we can assume that these data are normally distributed . • Also, since the median is approximately equal to the mean , we know that the distribution is symmetrical . Chapter 6 – 5 The Shape of a Normal Distribution: The Normal Curve Chapter 6 – 6 The Shape of a Normal Distribution Notice the shape of the normal curve in this graph. Some normal distributions are tall and thin , while others are short and wide . All normal distributions, though, are wider in the middle and symmetrical. Chapter 6 – 7 Notice that the standard deviation changes the relative width of the distribution ; the larger the standard deviation, the wider the curve....
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This note was uploaded on 07/13/2011 for the course SOC 301 taught by Professor Heberle during the Spring '11 term at University of Louisville.
 Spring '11
 Heberle

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