Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
9.7: Standard Deviation Analyzing Data Consider these sets of data: 60, 70, 80, 90, 100 The mean is: 80 78, 79, 80, 81, 82 The mean is: 80 Average or Mean doesn’t always tell the whole story! That’s where standard deviation comes into play. Standard Deviation tells us how spread out our data is. ___________ Standard Deviation The higher the standard deviation is, the more the data is varied, therefore less reliable making it ______________. The lower the standard deviation is, the more consistent your data is, more reliable making it ________________. Steps to find standard deviation 1. Find the mean of your data (the average!) We’ll call it m. 2. Take the difference between each member of the set and the mean. x-m 3. Square each of these numbers. (x – m)2. Steps to find standard deviation (continued) 4. Take the average of this set of numbers. (this is called the variance _______). 5. Take the square root of this number…. now you’ve found the standard deviation. Ex. 1: x 2 6 7 9 11 2, 6, 7, 9, 11 Mean: m = 7 (x – m) (x – m)2 -5 -1 0 2 25 4 16 1 0 4 Variance: 9.2 Standard Deviation: 3.03 Ex. 2: x 90 65 78 92 84 90, 65, 78, 92, 84 Mean: m = 81.8 (x – m) (x – m)2 Variance: 8.2 -16.8 -3.8 10.2 67.24 94.56 282.24 14.44 104.04 Standard Deviation: 2.2 4.84 9.72 Which of the previous sets of data would be more reliable? Compare Standard Deviations!!! 3.03 and 9.73 Data is less varied so more reliable!!