Square the differences from step 2 \u00e0 new column We do this because the sum of

Square the differences from step 2 à new column we

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3. Square the differences from step 2 à new column - We do this because the sum of the differences column will always be zero 4. Add up the total of the squared values - Ex: (0 + 625 + 225 + 225 + 625) = 1,700 - AKA sum of squares 5. Divide sum of squares (1700) by (n-1) - Where n = number of data points in beginning - Ex: (1700) ¸ (5-1) = 425 - Technically, the result is in units squared Standard Deviation – the square root of the variance Formula: Ö variance The unit of measure for the standard deviation is the same as the unit for the original data Measures the average distance b/w all of a set’s data points and the mean With variance, measuring how far on average each data value is from the mean of the sample Other Notes The standard deviation and variance should NEVER be negative values (this would be a mistake) Short-Cut Formulas for the Sample Variance and Standard Deviation Step-by-step 35 10 50 20 60 1. Sum the data values - Ex: (35 + 10 + 50 + 20 + 60) = 175 2. Square the result found in step 1 - Ex: (175)² = 30,625 3. Square each of the original data values
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4. Sum the squared column you created in step 3 - Ex: (1225 + 100 + 2500 + 400 + 3600) = 7,825 5. [(4 answer) – (2 answer ¸ # data points)] ¸ (n-1) - Ex: (7825 - 30,625/5) ¸ (4) = 425 The Variance and Standard Deviation for a Population The Population Variance Instead of (n-1) on the bottom of the equation, just use N N = total number of data points in the population Population Standard Deviation Square root of population variance Using Excel to Calculate the Variance and Standard Deviation The Sample Functions =VAR (data values) =STDEV (data values) Finding Sample Variability Data Analysis (add-in) > Descriptive Statistics Select input range for all data points Output Range (random selection) Summary Statistics > gives standard deviation, sample variance, and range values The Population Functions =VARP (data values) =STDEVP (data values) Ø 3.3 – USING THE MEAN AND STANDARD DEVIATION TOGETHERS o Some Notes § When means are similar / same, compare their standard deviations § When sample means are very different, comparing standard deviations can be misleading - b/c size of standard deviation is affected by the scale of the data The Coefficient of Variation Coefficient of Variation – (CV) measures the standard deviation in terms of its percentage of the mean High CV = high variability, less consistency Low CV = low variability, more consistency Best when comparing consistency b/w two data sets when their means are very different - b/c 2 data sets are likely to have diff means
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Gives a common measure – percentage – to compare 2+ things Measures the standard deviation in terms of its percentage of the mean Formula for the Sample Coefficient of Variation CV = S ¸ X (100) S = the sample standard deviation X = the sample mean Formula for the Population Coefficient of Variation CB = σ ¸ µ σ = the population standard deviation µ = the population mean The z-Score Z-Score
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