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Revisiting Statistics

Revisiting Statistics. What is the difference between descriptive and inferential statistics?. Descriptive Statistics: Describe data Help us organize bits of data into meaningful patterns and summaries Tell us only about the sample we studied Inferential:

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Revisiting Statistics

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  1. Revisiting Statistics

  2. What is the difference between descriptive and inferential statistics? • Descriptive Statistics: • Describe data • Help us organize bits of data into meaningful patterns and summaries • Tell us only about the sample we studied • Inferential: • Allow us to determine whether or not our findings can be applied to the larger population from which the sample was selected

  3. What is the difference between a frequency polygon and histogram? • Frequency polygon = line graph • Histogram = bar graph • Charting HOW OFTEN a score occurs • Frequency (number of times something occurs) is always on the y axis

  4. Why is the mean not always a “good” number to use to represent our data? • Does not take into account extreme outliers • Bill Gates walks into a coffee shop. The average income of all patrons soars. Median wealth remains unchanged. • 19/20 of your friends have a car valued at $12,000, but another has a car valued at 120,000 • Mean is 17,400 • Not best measure; median is better

  5. What is the range? • Distance between highest and lowest score • Tells us how spread out our scores are • Highest score – Lowest Score

  6. Standard Deviation • Tells us how clustered our scores are around the mean • Average distance of any score to the mean • Less variability = more confidence in our mean • Example: Basketball player averages 15 pts a game • Are you more confident if their range is • Between 13-17 pts in first 10 games • Between 5-25 pts in the first 10 games? • Higher the standard deviation, the farther from the mean scores are are and vise versa • Calculated as the square root of the variance • Variance will be given to you • Standard deviation for variance of 25 is… • 5

  7. Example for your test scores… • Unit 1 • Mean: 80% • Median: 83% • SD: 4.3 • Unit 2 (Bio) • Mean: 82% • Median: 83% • SD: 4.75 • Unit 3 (Sensation and Perception) • Mean: 81% • Median: 84% • SD: 5.7 • Unit 4 (States of Consciousness) • Mean: 88% • Median: 88% • SD: 4.62

  8. Unit 5 (Learning) • Mean: 82% • Median: 86% • SD: 5.21 • Unit 6 (Cognition) • Mean: 81% • Median: 84% • SD: 6.64 • Unit 7 (Motivation and Emotion) • Mean: 87% • Median: 90% • SD: 4.02

  9. Unit 8 (Development) • Mean: 83% • Median: 84% • SD: 4.93 • Unit 9 (Personality) • Mean: 79% • Median: 80% • SD: 5.53

  10. Standard deviation example • How much do employees at small businesses make? • 40,000 • 45,000 • 47,000 • 52,000 • 350,000 • Mean = 106,800 • Standard deviation = 136,021; Average difference between a score and the mean is 136,021 • Discard the extreme score, SD is now 4,966.56 • Distribution of first four is tightly clustered, distribution of all five is spread out

  11. Draw and label a normal curve for intelligence

  12. Where are the mean, median, and mode on a normal curve?

  13. Is the mean on a normal curve always 100? • No. • Doesn’t matter what number mean is • 68% of all scores will still fall within one standard deviation above and below the average • 96% of all scores will still fall within 2 standard deviations above or below the mean

  14. Skewed distributions • What if our data don’t follow a normal curve? • Positively or Negatively skewed (hump isn’t in the middle)

  15. Negatively (left) Skewed Distribution • There are low outliers • Hump is to the RIGHT • Mean is brought down (to the left of the hump) • Mode is ALWAYS at highest point • Median is also lower than the hump

  16. Positively (right) Skewed Distribution • There are HIGH outliers • Hump is to the LEFT • Mean is brought UP (to the right of hump) • Median is higher than hump • Mode is ALWAYS the highest part of the hump

  17. Practice Time

  18. Which has the greatest standard deviation? • A. 5, 10, 15, 20, 25 • B. 2, 4, 6, 8, 10 • C. 1, 7, 10, 18, 29 • D. 1, 2, 3, 4, 5 • E. 2, 7, 10, 11, 16

  19. What is the range of the following scores? • 5 • 8 • 9 • 2 • 10

  20. The Mean for a test is 50. Standard Deviation is 5. • What percentage of the scores are below 45? • What percentage of the scores are above 60?

  21. Z-scores • Used to compare scores from different distributions • Can convert scores from the different distributions into z scores. Z scores measure the distance of a score from the mean in units of standard deviation • Scores below the mean have negative z scores • Scores above the mean have positive z scores • Amy scored a 72 on a test with a mean of 80 and SD of 8, her z score is -1 • Clarence scored an 84 on the test, his z score is +.5

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