Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 4.notebook - Germantown School District
Document related concepts
Transcript
Chapter 4.notebook October 18, 2016 4.2 – Describing Variability in a Data Set (SPREAD) • • • • • 24 Deviation Standard Deviation Variance Range Interquartile range © 2008 Brooks/Cole, a division of Thomson Learning, Inc. Describing Variability The simplest numerical measure of the variability or spread of a numerical data set is the range, which is defined to be the difference between the largest and smallest data values. range = maximum minimum Would this be a "resistant" measure of spread? 25 © 2008 Brooks/Cole, a division of Thomson Learning, Inc. Chapter 4.notebook October 18, 2016 Describing Variability We can also describe variability by finding out how each data value compares to the mean. We call these values the Deviations from the sample mean: Note: If a value is below the mean the deviation will be negative and positive if the value is greater than the mean. The sum of all of the deviations from the sample mean will be equal to 0, except possibly for the effects of rounding the numbers. This means that the average deviation from the mean is always 0 and cannot be used as a measure of variability. 29 © 2008 Brooks/Cole, a division of Thomson Learning, Inc. Sample Variance The sample variance, is the sum of the squared deviations (Sxx) from the mean divided by n1. 30 © 2008 Brooks/Cole, a division of Thomson Learning, Inc. Chapter 4.notebook October 18, 2016 Sample Standard Deviation The sample standard deviation, denoted "s" is the positive square root of the sample variance. Standard deviation always has the same units as the units from the observations. We divide by n1 because it has been shown that the value is closer to the true population value than dividing by n. **Population standard deviation is denoted as _____ Standard deviation can be thought of as the size of the "typical" deviation from the mean. 31 © 2008 Brooks/Cole, a division of Thomson Learning, Inc. Example calculations 10 Macintosh apples were randomly selected and weighed (in ounces). Sum of columns: 32 Chapter 4.notebook October 18, 2016 Calculator Formula for s2 and s A little algebra can establish the sum of the square deviations, A computational formula for the sample variance is also given by 33 © 2008 Brooks/Cole, a division of Thomson Learning, Inc. Calculations Revisited 34 © 2008 Brooks/Cole, a division of Thomson Learning, Inc. Chapter 4.notebook October 18, 2016 Is standard deviation resistant to the presence of outliers? Using the TI for Mean, Median, Quartiles, and Standard Deviation • • • • Enter the data into a list Press Stat > Calc > #1: 1Var Stats If the list is in L1, just press enter If the list is in another list you will need to select it from the List Menu (2nd Stat), then press enter • Arrow down to see the complete listing of the stats • ALWAYS report the value of Sx on your calculator for standard deviationb 36 © 2008 Brooks/Cole, a division of Thomson Learning, Inc.
