1. Numbers about Numbers Lesson #19 Chapter 4

2. With every set of numeric data, you can compute… Mean Devia tions Squar e of the Devia tions Varian ce Stand ard Devia tion

3. When you have a data set…

4. 1. The sum is 25.40 2. The number of terms is 10 3. The mean is 2.54 1. The sum is 25.40 2. The number of terms is 10 3. The mean is 2.54

5. X X Bar Deviat ion ( X – X Bar ) 2.002.54-0.54 3.202.540.66 1.802.54-0.74 2.902.540.36 3.602.541.06 0.902.54-1.64 4.002.541.46 3.302.540.76 2.902.540.36 0.802.54-1.74 The distance a number is away from the mean is called its deviation

6. Variance describes how spread apart all of the values are. Since the sum of the deviations is 0 (always), it doesn’t make sense to use this. X X – X Bar ( Devia tion ) ( X – X Bar ) ² 2.00-0.540.2916 3.200.660.4356 1.80-0.740.5476 2.900.360.1296 3.601.061.1236 0.90-1.642.6896 4.001.462.1316 3.300.760.5776 2.900.360.1296 0.80-1.743.0276 Instead, the variance is calculated by taking the sum of the squared deviations and dividing by n - 1.

8. Finally, the value which represen ts the average distance all the numbers are from the mean is called the standard deviatio n. This is the square root of the value of the variance.

9. 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.

10. Try this one… The salaries of 8 public school teachers: 1) 46,098 2) 36,259 3) 35,084 4) 38,617 5) 42,690 6) 26,202 7) 47,169 8) 37,109 Calculate the following 1) The mean (to the nearest hundredth) 2) Each deviation (to the nearest hundredth) 3) The square of each deviation (to the nearest thousandth) 4) The sum of the square of each deviation (to the nearest thousandth) 5) The variance (to the nearest thousandth) 6) The standard deviation (to the nearest thousandth) Show the steps for each calculation.

11. Now continue your calculati ons with the Class Olympics data gathered this week with the concepts presented in the lesson.