1. Ch. 3 – part 1 Measures of central tendency Measures of variation Calculating standard deviation Using the TI30XII ma260notes_ch3_calc_directions.pptx

2. Notation- sample and population sizeMeanVariationStandard 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, midrange 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. Find the approximate mean, median, mode on these distributions Symmetric UniformBimodal Skewed Left Skewed Right

8. Skewed distributions and measures of central tendency

9. 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

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

11. Measures of variation Range= Sample Standard deviation = s =

12. Basic formulas sizeMeanVarianceStandard deviation (algebraically equivalent) Population N = = Sample n = s 2 theoretical s = Computation-shortcut s =

13. Sample Standard deviation (s) formulas– Theoretical formula calculation formula S = =

14. Optional: Proof that the 2 s formulas are algebraically equivalent

15. Use theoretical formula to find st dev (s) Class 1 100 90 70 50 40 Class 2 72 71 70 69 68

16. 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

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

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

19. What does s mean? For the previous example, calculate: Mean + s = Mean – s =

20. Using your TI30XIIS or TI30XIIB for One variable statistics (using Ex #4) 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…

21. TI30XII 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.

22. Basic info on using the TI83 instead: 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

23. Ex 6: Use calculation formula for s X 2 3 7 12 15 16 Now, verify mean and s on your calculator

24. Example #6: 112.8 141.3 198.9 200.4 87.5 When the mean isn’t an integer, the theoretical formula is messier. Try another example using only the computational formula for s. This is the one we’ll usually use: Data set: 112.8 141.3 198.9 200.4 87.5 Calculate the mean. You should get 148.18

25. Calculate s, using shortcut formula x i x i 2 112.8 12723.84 141.3 19965.69 198.9 39561.21 200.4 40160.16 87.5 7656.25 Sum=740.9 sum=120,067.15 s = = = 50.7 Now, verify your work using the TI30XII.