1. Ch. 12 – part 1B Measures of central tendency Measures of variation Shapes of distributions Calculation standard deviation Using the TI30XII

2. Notation- sample and population sizeMeanStandard deviation Sample n s Population N 

3. Measures of Central Tendency-- Averages Find the average for the following test scores: Ex. #1: 78 83 97 32 75 45 52 How should we measure the average?

4. 78 83 97 32 75 45 52 Mean Median Mode Midrange

5. Ex. #2: Find mean, median, mode SalaryFrequency 10,0001 20,0004 30,0003 250,0001

6. Ex #3: GPAs – calculate ClassGrade# credits MathB (3.0)4 EnglishC (2.0)2 PhysicsA (4.0)5

7. Skewed distributions and measures of central tendency

8. Ex. #4: Find the mean and median for each of the 2 examples Class 1 100 90 70 50 40 Class 2 72 71 70 69 68

9. How do they vary?-- Range Class 1 100 90 70 50 40 Class 2 72 71 70 69 68

10. Measures of variation Range= Sample Standard deviation (Theoretical) = s =

11. Standard deviation- Use theoretical formula to find s. Then find mean + s and mean – s. Class 1 100 90 70 50 40 Class 2 72 71 70 69 68

12. Example #5- Mean and s Try an example using both the theoretical formula and the computational formula for s: Data set: 1 1 2 4 7 Calculate the mean. You should get 3

13. Ex #5-- Theoretical formula Use the theoretical formula for s x i 2

14. A second formula- the computational formula for s Sometimes the theoretical calculations get messy, and we shouldn’t round in the middle of the problem. So we will need a computational formula which is algebraically equivalent. (It takes 5 steps of algebra). S = = theoretical computational

15. Ex # 5 -- Computation formula Use the computational formula for s X i x i 2

16. 3 rd approach: Using your TI30XIIS for 1-Var Stats (using Ex #5) Considering the following data set, calculate sample mean and sample standard deviation: 1 1 2 4 7 Here are the key strokes: 1.Clear previous data with [EXIT STAT]: push [2nd] and then [STAT VAR] (If you get an Error, hit CLEAR). 2.Enter Statistics mode by hitting: the [2 nd ]button followed by [DATA] 3. Hit [=] to accept One-Variable Mode. 4. Hit the [DATA] button and it is ready for you to enter your first value when it prompts X 1 = 5. Type in the first piece of data (in this case it is 1). 6. Hit the “down arrow” button to accept the piece of data. 7. …

17. Directions continued 7.When it say FRQ=1 (i.e. frequency is one) hit the “down arrow” button again 8. Now enter in your second piece of data when it prompts X 2 = 9. Keep entering in data with frequencies of 1 until all of the data is in the calculator. (In this case, after the 5 data values, the calculator prompts X 6 =). 10. Hit the [STATVAR] button. 11.Use your right arrow to find the sample mean and sample standard deviation (s x =2.55) 12.Clear data again with [EXIT STAT]: Hitting [2 nd ] followed by [STATVAR] will prompt you to leave the statistics mode. Hit [=] to leave statistics mode. You are now ready to start a new data set.

18. To use the TI83: Go to STAT/Edit: Pick 4. Type "ClrList L1" Go to STAT/Edit Pick 1. Edit. Enter your list of numbers. Go to STAT/CALC and pick 1. 1-Var Stats

19. Ex #6: find st dev (s) with computational formula 6 6 6 6 7 7 7 4 8 3 Verify your work on a calculator

20. Ex. #7: use calculator to find mean, s: 78 73 84 72 66 42 99 67 62 45 89 76 43 98 56 78 66 54 88 67 90 Also, find mean + s mean - s Review stem/leaf

21. Ex. #8: Use the calculator to find s 73 58 68 75 94 87 83 89 52 99 95 77 75 81 75 69 76 77 71 50 Use the calculator to find s Find mean + s= mean – s =