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

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

Measures of Central Tendency-- Averages Find the average for the following test scores: Ex. #1: How should we measure the average?

Mean Median Mode Midrange

Ex. #2: Find mean, median, mode SalaryFrequency 10, , , ,0001

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

Skewed distributions and measures of central tendency

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

How do they vary?-- Range Class Class

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

Standard deviation- Use theoretical formula to find s. Then find mean + s and mean – s. Class Class

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

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

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

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

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: 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. …

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.

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

Ex #6: find st dev (s) with computational formula Verify your work on a calculator

Ex. #7: use calculator to find mean, s: Also, find mean + s mean - s Review stem/leaf

Ex. #8: Use the calculator to find s Use the calculator to find s Find mean + s= mean – s =