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With every set of numeric data, you can computeβ¦ Mean Variance Deviations Standard Deviation Square of the Deviations The mean of a data set is calculated by finding the sum of the numbers and dividing by the number of entries. It is also known as the average. It is represented by the symbol π₯β¦ Example: These are 10 Grade Point Averages: 2.00 3.20 1.80 2.90 3.60 0.90 4.00 3.30 2.90 0.80 Find the meanβ¦ When you have a data setβ¦ 1. The sum is 25.40 2. The number of terms is 10 3. The mean is 2.54 The distance a number is away from the mean is called its deviation X X Bar Deviation (X β X Bar) 2.00 2.54 -0.54 3.20 2.54 0.66 1.80 2.54 -0.74 2.90 2.54 0.36 3.60 2.54 1.06 0.90 2.54 -1.64 4.00 2.54 1.46 3.30 2.54 0.76 2.90 2.54 0.36 0.80 2.54 -1.74 X X β X Bar (Deviation) (X β X Bar)² 2.00 -0.54 0.2916 3.20 0.66 0.4356 1.80 -0.74 0.5476 2.90 0.36 0.1296 3.60 1.06 1.1236 0.90 -1.64 2.6896 4.00 1.46 2.1316 3.30 0.76 0.5776 2.90 0.36 0.1296 0.80 -1.74 3.0276 Variance describes how spread apart all of the values are. Since the sum of the deviations is 0 (always), it doesnβt make sense to use this. Instead, the variance is calculated by taking the sum of the squared deviations and dividing by n - 1. (π β π)π = π. ππππ + π. ππππ + π. ππππ + π. ππππ + π. ππππ +π. ππππ + π. ππππ + π. ππππ + π. ππππ + π. ππππ =11.084 The Variance (s²) = ππ.πππ πβπ β1.2316 = ππ.πππ π Finally, the value which represents the average distance all the numbers are from the mean is called the standard deviation. This is the square root of the value of the variance. π = 1.2316 β 1.1098 Going back to the original data, we can say that the average distance all grade point averages are from the mean (2.54) is approximately 1.11 grade points. The closer the value of the standard deviation is to 0, the closer the values of the data are to the mean. The farther the value of the standard deviation is from 0, the more spread out the data is around the mean. Try this oneβ¦ The salaries of 8 public school teachers: 1) 2) 3) 4) 5) 6) 7) 8) 46,098 36,259 35,084 38,617 42,690 26,202 47,169 37,109 Calculate the following 1) The mean 2) 3) 4) 5) 6) (to the nearest hundredth) Each deviation (to the nearest hundredth) The square of each deviation (to the nearest thousandth) The sum of the square of each deviation (to the nearest thousandth) The variance (to the nearest thousandth) The standard deviation (to the nearest thousandth) Show the steps for each calculation. Now continue your calculations with the Class Olympics data gathered this week with the concepts presented in the lesson.