Chapter 5 Normal Curve and Standard Scores

1. Chapter 5 Normal Curve and Standard Scores James A. Van Slyke Azusa Pacific University

2. Frequency Distributions Graphs • Histograms • Vertical bars above each score • Height of bar corresponds to Frequency • Width extends to real limits of the score • Bar graphs • Vertical bars above each score with space between each bar • Designates separate distinct categories

3. Frequency Distribution Tables

4. Histogram Frequency

5. Bar graph Frequency

6. DISTRIBUTIONS AND GRAPHS • Frequency Distribution Polygon (line graph) • A dot is centered above the score w/ height corresponding to frequency • Connected with a continuous line

7. Line graph (frequency distribution polygon) Frequency

8. DISTRIBUTIONS AND GRAPHS • Normal Curve • Symmetrical – when folded, the two sides match • “Bell-shaped Curve”

9. Symmetrical Distribution Frequency

10. Skewed • Skewed – When folded the curve does not match • Positive skew – Most scores occur at the lower values of the horizontal axis • Negative skew – Most scores occur at the higher end of the horizontal axis

11. Positive Skew Frequency

12. Negative Skew Frequency

13. Measuring Central Tendency • If a particular distribution is unimodal and symmetrical • Mean, median, and mode are equal • bell-shaped curve; normal curve • Skewed distribution • Mean and median are not equal • Positive – mean larger than the median • Negative – mean is smaller than the median

14. Properties of the Normal Curve • Midpoint is mean, median and mode • Inflection points • One on each side of the mean • Notes where the curve changes direction • The inflection points are one standard deviation from the mean

15. Properties of the Normal Curve • In a normal curve • 34.13% of the scores are within the area between the mean and the score at one standard deviation • 13.59% of the scores lie between one and 2 standard deviations • 2.15% of the scores lie between two and three standard deviations • The same is true going in the negative direction

16. Standard or z scores • The transformation of a raw score into a score that reflects it’s relationship to the mean • This score designates how many standard deviations a particular score is above or below the mean • This process is referred to as score transformation

17. Standard or z scores • In equation form, a z score is calculated by:

18. Standard Scores • Allow us to know either the percentage of scores above and below a particular score • Allows us to transform two sets of scores into the same comparable scores

19. Z scores • Scores have the same shape as the raw scores • The mean of z scores always equals zero • The standard deviation of z scores always equals one

20. Converting Z score • Convert a z score into a percentage • Draw a diagram of the score on a z curve • consult the chart in appendix D, pg. 552 • Solve for the Area • May be used to find percentage between two scores • Also locate percentage above or below a certain score

21. Raw Scores from z scores • Find the raw score associated with a z score • Raw score associated with a z of .52

22. Homework • Chapter 5 • Page 110 – 8,11,12,16,17