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Test 1 Review - Test 1 Review...

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Test 1 Review Presentation, Stats, Michael J. Clark
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Calculating Means
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Example Our sample data set is the following: 900, 905, 1005, 1005, 1100, 1120, 1201
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example In order to calculate the sample mean we  simply get a sum and divide by the  number of entries. 900+905+1005+1005+1100+1120+1201=SUM SUM / 7  = Sample Mean  1033.71429
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Calculating Modes
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Example Our sample data set is the following: 100, 105, 105, 110, 120, 120 What is the mode?
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example The mode is the number that occurs  most frequently. So, our mode is:      105 and 120
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example Remember, there can be multiple modes  or no mode at all.
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Finding the Range
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Example Here is your data: 14, 90, 27, 18, 29, 76, 76, 82 
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Example Here is your data: 14, 90, 27, 18, 29, 76, 76, 82     For this set of numbers we must remember to  order the #’s.  In order to find the range we  need the highest and lowest numbers. 14 is our lowest, 90 is our highest, is this our  range?
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Example   Our range is 76.  We subtract the lowest  value from the highest.   The range is a measure of spread, it  does not deal with where the numbers  fall, a similar set of data with a range of  76 is given below. 8,011      8,039     8,087    8,018
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Sample Variance and  Standard Deviation  Calculations
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Steps for Standard Deviation Compute the difference between each  value and the mean. Square each difference Add the squared differences Divide this total by n-1 to get the sample  variance. Take the square root of the sample  variance.
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Standard Deviation Sample Mean = 100 Sample: 100, 99, 101, 103, 97, 100 How do you calculate the Standard  Deviation???
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Calculating the Standard Deviation 100-100 = 0 0 2     =     0 101-100 = 1 1 2    =      1 99-100 = -1 -1 2   =     1 103-100 = 3 3 2     =     9 100-100 = 0 0 2     =     0 97-100 = -3 -3 2   =     9 9+9+1+1+0+0 = 20   20 / 5 = 4 S = 2
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Answers Variance of 4 Standard deviation of 2
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The Empirical Rule
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The Empirical Rule You can use the empirical rule when you have a  bell-shaped distribution Bell shaped distribution: symmetrical data set where the median and mean  are the same which creates a “bell shape” to the distribution. The Empirical Rule states: 68% of all values are within 1 standard deviation of the mean 95% of all values are within 2 standard deviations of the mean 99.7% of all values are within 3 standard deviations of the mean.
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Interquartile Range
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