Notes 2.7: Standard Deviation



Learning Target Standard Deviation? I can calculate the standard deviation of a data set ?Standard Deviation: Approximately thought of as the average distance each value is from the meanThere are two standard deviations: One for a population and one for a sample (their formulas differ slightly). We will be calculating the standard deviation of a sample.2428875146050sx=?(x-x)2(n-1)00sx=?(x-x)2(n-1)To find standard deviation:Step 1: Find the mean of the numbers.Step 2: For each number (individually), subtract the mean.Step 3: Square each of these differences (individually).Step 4: Add these answers together (of the squared difference between the value and the mean).Step 5: Divide by 1 less than the number of values in your data set. This gives you the variance.Step 6: Take the square root. This gives you the standard deviation.Note: It is helpful to use a table to break down this formula into smaller steps!Example 1: Find the standard deviation of the following heights from 10 students in the classroom.586062636465656668702697480889000Fill in the values for x to begin (L1).Step 1: Find x = _________Step 2: Subtract x from each value in L1 (L2) Step 3: Square the answers in L2 (L3)Step 4: Add the values in L3Step 5: Divide the sum by n - 1This answer is the varianceStep 6: Take the square root of the varianceThis answer is the standard deviation Step 3 Variance = (x-x?)2n-1 = _______Standard Deviation = varianceStandard Deviation = (x-x)2n-1 = _____Example 2: Fill in the table and find the variance and standard deviation for the following set of numbers:1122334425493872095500x = _______Variance = (x-x?)2n-1 = _______ Standard Deviation = (x-x)2n-1 = ______? I can determine the appropriate measure of spread to use based on the data set ?Skewed DataSymmetric DataMeasure of CenterMedianMeanMeasure of SpreadRange/IQRStandard DeviationExample 3: Determine the measure of spread that is most appropriate for each histogram.3543305080000289750513335005166360952500 ................
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