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Statistics Recording the results from our studies.

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Descriptive Statistics Just describes sets of data. You might create a frequency distribution. Frequency polygons or histograms.

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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

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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

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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

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Let’s say you are looking to move to a new place…. The average income of a family in the new city is 70,000 – not too bad…. However…. 26 families make less than 70,000 Only 3 families make more than 70,000

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Skewed Distributions 15 20 25 30 35 40 45 50 90 475710 70 Mode Median Mean One Family Income per family in thousands of dollars

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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)

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Measures of Variation

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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?

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Calculating the Standard Deviation 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 Data: 2,2,4,8

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Normal Distribution In a normal distribution, the mean, median and mode are all the same.

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Normal Distribution A standard deviation of 15 accounts for about 68% of responses. A normal distribution is a bell shaped curve.

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Statistical Significance How likely it is that an obtained result occurred by chance Odds must be less than 5% (p<.05) in order for results to be statistically significant This means that your results are 95% (p>.95) a result of your IV

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