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Statistics Recording the results from our studies. Descriptive Statistics • Just describes sets of data. • You might create a frequency distribution. • Frequency polygons or histograms. Measures of Central Tendency • Mode – score that occurs most often EX: 3,5,5,7,5,4,9,6,8,7,10 5 is the mode • Median – score in the halfway point EX: 3,4,5,5,5,6,7,7,8,9,10 6 is the median • Mean – average score EX: 3+5+5+7+5+4+9+6+8+7+10=69 69/11 6.27 is the mean Mean, Median, Mode • The weekly salaries of six employees at McDonalds are $140, $220, $90, $180, $140, $200. – For these six salaries, find: • (a) the mean • (b) the median • (c) the mode Mean, Median, Mode • Answers Mean: 90+ 140+ 140+ 180 + 200 + 220 =$ 161.67 6 Median: 90,140,140,180,200,220 The two numbers that fall in the middle need to be averaged. 140 + 180 = 160 2 Mode: 90,140,140,180,200,220 The number that appears the most is 140 Central Tendency • Watch out for extreme scores or outliers. Let’s look at the salaries of the employees at Dunder Mifflin 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. Statistical Reasoning A Skewed Distribution 15 20 25 30 35 40 45 50 90 475 70 Mode Median One Family Mean Income per family in thousands of dollars 710 Distributions • 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) Normal Distribution • In a normal distribution, the mean, median and mode are all the same. Other measures of variability • Range: distance from highest to lowest scores. • Standard Deviation: the variance of scores around the mean. Shaq and Kobe may both score 30 ppg (same mean). • The higher the variance or SD, the But their SDs are very different. more spread out the distribution is. • Do scientists want a big or small SD? Calculating the Standard Deviation Data: 2,2,4,8 1. Figure out the Mean: 16 4 = 4 2. Take mean & figure out difference from each point: 2-4=-2, 2-4=-2, 4-4=0, 8-4=4 3. Square each difference:4,4,0,16 4. Add together: 4+4+0+16=24 5. Divide by #: 24 4 = 6 This is the variance 6. Take square root: 2.45 Normal Distribution A normal distribution is a bell shaped curve. A standard deviation of 15 accounts for about 68% of responses. Scores • A unit that measures the distance of one score from the mean. • A positive z score means a number above the mean. • A negative z score means a number below the mean. Statistical Significance • How likely it is that an obtained result occurred by chance • Odds must be less than 5% (.05) in order for results to be statistically significant • This means that your results are 95% (.95) a result of your IV