MTH 120 - Calculating Var & St Dev plus Example

MTH 120 - Calculating Var & St Dev plus Example -...

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Calculating the Mean REMEMBER: The frequency is the Calculating the Variance and Standard Deviation NOTE (1) Wh l l ti th i lti l th l (d t ) 2 REMEMBER: The frequency is the number of times a specific value (2) Since the problem asks us to round to 2 DP, we will cautiously round only our second to last calulcation to 2+2 (or 4) DP, but all other calculations will be done with "exact" values. occurred; e.g., we know from the received a 70 on their test. table below that 3 students NOTE: (1) When calculating the variance, we multiply the value (data mean) times the frequency just like we did when we calculated the mean. TSCR FREQ TSCR FREQ 70 3 70 x 3 = 210 70 ( 70 1360/27 ) 2 = 385.322359396433… = 385.3224 3 385.3224 x 3 = 1155.9672 60 5 60 x 5 = 300 60 ( 60 1360/27 ) 2 = 92.7297668038408… = 92.7298 5 92.7298 x 5 = 463.6490 be done with exact values. TSCR x FREQ = … (TSCR MEAN) 2 x FREQ = … (TSCR MEAN) 2 = … 50 11 50 x 11 = 550 50 ( 50 1360/27 ) 2 = 0.137174211248288… = 0.1372 11 0.1372 x 11 = 1.5092 40 6 40 x 6 = 240 40 ( 40 1360/27 ) 2 = 107.544581618656… = 107.5446 6 107.5446 x 6 = 645.2676 30 2 30 x 2 = 60 30 ( 30 1360/27 ) 2 = 414.951989026063… = 414.9520 2 414.952 x 2 = 829.9040 27 1360 27 3096.297 Mean = 1360/27 = 50.370370370… 50.4 NOTE: Use "1360/27" for the Variance = 3096.2970/27 114.68 and SD = SQRT(114.68) 10.71 variance to avoid rounding error mean when calculating the
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Finding the Variance and Standard Deviation The procedure for finding the standard deviation that is presented in the textbook ሺi.e., the green box belowሻ works well for finding the standard deviation of a list of numbers; however, the procedure does not lend itself to data presented in a frequency table.
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