Transcript Statistics
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 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 Skewed Distributions 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) Measures of Variation 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? 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 • In a normal distribution, the mean, median and mode are all the same. Normal Distribution A normal distribution is a bell shaped curve. A standard deviation of 15 accounts for about 68% of responses. 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