Ch. 12 – part 1B

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

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

6. Ex #3: GPAs – calculate

7. Skewed distributions and measures of central tendency

8. Ex. #4: Find the mean and median for each of the 2 examples

9. How do they vary?-- Range

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.

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 xi   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 Xi                xi2

16. 3rd 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: • Clear previous data with [EXIT STAT]:  push [2nd] and then [STAT VAR] (If you get an Error, hit CLEAR). • Enter Statistics mode by hitting: the [2nd]button followed by [DATA] •  Hit [=] to accept One-Variable Mode. •  Hit the [DATA] button and it is ready for you to enter your first value when it prompts X1= •  Type in the first piece of data (in this case it is 1). •  Hit the “down arrow” button to accept the piece of data. • …

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 X2= 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 X6=). •  Hit the [STATVAR] button. • Use your right arrow to find the sample mean  and sample standard deviation (sx=2.55) • Clear data again with [EXIT STAT]:  Hitting [2nd] 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 "ClrListL1" • 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 =