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## Formula

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**Compute a standard deviation with the Raw-Score Method**• Previously learned the deviation formula • Good to see “what's going on” • Raw score formula • Easier to calculate than the deviation formula • Not as intuitive as the deviation formula • They are algebraically the same!!**Raw-Score Formula**Note: This is the formula for both and S**Step 4: Plug in values**N = 5 X = 44 X2 = 640**Step 4: Plug in values**5 5 N = 5 X = 44 X2 = 640**Step 4: Plug in values**44 5 5 N = 5 X = 44 X2 = 640**Step 4: Plug in values**44 640 5 5 N = 5 X = 44 X2 = 640**Step 5: Solve!**1936 44 640 5 5**Step 5: Solve!**1936 44 640 387.2 5 5**Step 5: Solve!**1936 44 50.56 640 387.2 5 5 Answer = 7.11**Practice**• Use the raw score formula and find the standard deviation of: 6, 3, 4, 10, 8**31**225 5 5 N = 5 X = 31 X2 = 225**1936**44 225 192.2 2.56 = 5 5**Ŝ**• What if we want to use a sample standard deviation to estimate the population ? • We need to make one small change to the formula to do this • You need to make the s an “unbiased estimator”**Ŝ**• To do that you use Ŝ • This provides an estimate of the populations variability**Remember**S =**Just “ - 1”**Ŝ= -1**Why?**• The first formula is biased -- its answer tends to be too small • Don’t worry about why -- unless you want too!!**Practice!**• Below is data from 5 people in this class. What is the estimated standard deviation of all the students in this class? Use the Ŝ raw score formula. • Neuroticism scores 12, 15, 22, 10, 9**68**1034 5 5 - 1 N = 5 X = 68 X2 = 1034**1936**44 1034 924.8 5.22 = 5 4**Variance**• The last step in calculating a standard deviation is to find the square root • The number you are fining the square root of is the variance! 2 = population variance Ŝ2 = sample variance used to estimate 2**Variance**S 2, 2 = Ŝ2 =**Variance**S 2, 2 = Ŝ2 = - 1**There are 12 different formulas!**• Standard Deviation • Deviation Formula , S, Ŝ • Raw Formula , S, Ŝ • Variance • Deviation Formula 2, S 2, Ŝ2 • Raw Formula 2, S 2, Ŝ2**Review -- Important Formulas**• Standard Deviation -- Deviation Formula = Ŝ =**Review -- Important Formulas**• Standard Deviation -- Deviation Formula**Review -- Important Formulas**• Variance -- Deviation Formula 2 = Ŝ2 =**Review -- Important Formulas**• Variance -- Deviation Formula 2**Review -- Important Formulas**• Standard Deviation -- Raw Formula and S = Ŝ = - 1**Review -- Important Formulas**• Variance -- Raw Formula 2 and S2 = Ŝ2 = - 1**How to know which to use**• 1) Does the question want a standard deviation or a variance (most of the time standard deviations are used) • 2) Is the group of scores a sample or population? • 3) If it’s a sample, do you want to generalize the findings to a population?**Practice**• You are interested in how citizens of the US feel about the president. You asked 8 people to rate the president on a 10 point scale. Describe how the country feels about the president -- be sure to report a measure of central tendency and the standard deviation. 8, 4, 9, 10, 6, 5, 7, 9**Central Tendency**8, 4, 9, 10, 6, 5, 7, 9 4, 5, 6, 7, 8, 9, 9, 10 Mean = 7.25 Median = (4.5) = 7.5 Mode = 9**Standard Deviation**• Want to use Ŝ**Standard Deviation**• Want to use Ŝ -1**Standard Deviation**• Want to use Ŝ 452 58 8 8 - 1 -1**Standard Deviation**• Want to use Ŝ 58 452 8 8 - 1 -1**Standard Deviation**• Want to use Ŝ 452 420.5 7 -1