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Statistics • Recording the results from our studies. • Must use a common language so we all know what we are talking about. Descriptive Statistics • Just describes sets of data. • You might create a frequency distribution. • Frequency polygons or histograms. Measures of Central Tendency (know this term) Mean = average of all scores or observations Median = the middle number when all scores are sorted from highest to lowest Mode = the score that appears most frequently in the data. Measures of Central Tendency Watch out for extreme scores or outliers. Let’s look at the salaries of the employees at Dunder Mifflen Paper in Scranton: $25,000-Pam $25,000- Kevin $25,000- Angela $100,000- Andy $100,000- Dwight $200,000- Jim $300,000- Michael • The median salary looks good at $100,000. • The mean salary also looks good at about $110,000. • But the mode salary is only $25,000. • Maybe not the best place to work. • Then again living in Scranton is kind of cheap. Normal Distribution • In a normal distribution, the mean, median and mode are all the same. Distributions Median • Outliers skew distributions. • If group has one high score, the curve has a positive skew (contains more low scores) • If a group has a low outlier, the curve has a negative skew (contains more high scores) Mean Median Mean Important Idea • The larger your sample size, the more likely it is your data will resemble a normal curve (because outliers will be mitigated). Seeing Statistics – Click on Contents – Go to 7.1 Other measures of variability • Range: distance from highest to lowest scores. • Standard Deviation: the variance of scores around the mean. • The higher the variance or SD, the more spread out the distribution is. • Do scientists want a big or small SD? Dwayne Wade and Kobe may both score 26 ppg (same mean). But their SDs are very different. 68% are within one standard deviation 95% are within 2 standard deviations 99.7 are within 3 standard deviations Correlation Remember the scatter plots! Positive Correlation right) (bottom left to upper Negative Correlation (upper left to bottom right) Practice Question #1 1.Which of the following events is the most probable? A) flipping 6 or more heads in 10 coin flips B) flipping 60 or more heads in 100 coin flips C)flipping 600 or more heads in 1000 coin flips D)All these results are equally probable. Practice Question #2 1. For which of the following distributions of scores would the median most clearly be a more appropriate measure of central tendency than the mean? A) 10, 22, 8, 9, 6 B) 12, 6, 8, 5, 4 C)12, 15, 12, 9, 12 D)23, 7, 3, 27, 16 What would be another way of asking this question? Practice Question #3 3. Professor Connolly uses a scatterplot to display the relationship between students' intelligence test scores and the number of failing grades they have received. The points on the plot are most likely clustered in a pattern that: A) resembles a Ushaped curve. B) extends from the upper left to the lower right of the plot. C)resembles a bellshaped curve. D)extends from the lower left to the upper right of the plot. Practice Question #4 4. In a single day, 45 babies were born in hospital X, 65 babies in hospital Y, and 25 babies in hospital Z. At which hospital is there the greatest probability that more than 60 percent of the babies are of the same sex? A) hospital X B) hospital Y C)hospital Z D)The probability is the same at all three hospitals. Practice Question #5 5. Approximately what percentage of the cases represented by the normal curve fall between –3 and +3 standard deviations from the mean? A) 34 B) 68 C)95 D)100 Practice Question #6 6. When Mr. Adams calculated his students' algebra test scores, he noticed that two students had extremely low scores. Which measure of central tendency is affected most by the scores of these two students? A) mean B) standard deviation C)mode D)median Practice Question #7 7. If IQ scores are normally distributed, having a mean of 100 and a standard deviation of 15, approximately what percentage of people have IQ scores somewhere between 70 and 130? A) 34 B) 50 C)68 D)95 Practice Question #8 8. What is the standard deviation if the variance is equal to 36? A) 4 B) 5 C)6 D)9 E) 36 Answers 1. 2. 3. 4. 5. 6. 7. 8. A A B C D A D C