Notes – Standard Deviation, Variance, and MAD

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Presentation transcript:

Notes – Standard Deviation, Variance, and MAD Algebra 1 Notes Notes – Standard Deviation, Variance, and MAD

Definition of Variance In a data set, the variance is the mean of the squares of the deviations. Variance for Population: sigma squared E represents the sum x is a single data entry u is the mean. N is the number of data

Definition of Standard Deviation In a data set, the standard deviation is the square root of the variance. Standard Deviation for Population: sigma E represents the sum x is a single data entry u is the mean. N is the number of data

Important Note We have been informed that we will calculate all statistics using the formulas for POPULATION.

Example 1: Calculate the variance and standard deviation. DATA 100 95 80 70 50 30

Calculator Directions for Mean, Median, and Standard Deviation Enter the data STAT Edit Enter numbers into List 1 (L1) Calculate mean, median, standard deviation CALC 1-VAR Stats ENTER The mean will be displayed as The standard deviation will be displayed as You will need to scroll down to get to the median. It will be displayed as Med The Variance will not be displayed on the screen; it must be calculated by squaring the standard deviation. The range will not be displayed on the screen; it must be calculated by subtracting: maxX – minX.

Example 1: Calculate the variance and standard deviation. DATA 100 100 – 75.625 = 24.375 (24.375)^2 = 594.14 594.14 95 95 – 75.625 = 19.375 375.39 80 4.375 19.141 70 -5.625 31.641 50 -25.63 656.64 30 -45.63 2081.6

Definition of Mean Absolute Deviation In a data set, the mean absolute deviation (MAD) is the mean of the absolute value of the deviations. MAD for Population E represents the sum x is a single data entry u is the mean. N is the number of data

Example 2: Calculate the mean absolute deviation. DATA 100 95 80 70 50 30

Calculator Directions for Mean Absolute Deviation Enter the data STAT Edit Enter numbers into List 1 (L1) Find the mean of the data points, CALC 1-VAR Stats ENTER In List 2 (L2), subtract the mean from each data point in L1 and then take the absolute value of the answer. Use the arrow keys to move cursor so that L2 is highlighted 2nd Zero ENTER 2nd 1 minus VARS 5 2 ) ENTER Find the mean of the values in L2 1-VAR Stats 2nd 2

Example 2: Calculate the mean absolute deviation. DATA 100 100 – 75.625 = 24.375 24.375 95 95 – 75.625 = 19.375 19.375 80 4.375 70 -5.625 5.625 50 -25.63 25.63 30 -45.63 45.63