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Ch. 12 – part 1B. Measures of central tendency Measures of variation Shapes of distributions Calculation standard deviation Using the TI30XII. Notation- sample and population. Measures of Central Tendency-- Averages. Find the average for the following test scores:
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Ch. 12 – part 1B Measures of central tendency Measures of variation Shapes of distributions Calculation standard deviation Using the TI30XII
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?
78 83 97 32 75 45 52 • Mean • Median • Mode • Midrange
Measures of variation • Range= • Sample Standard deviation (Theoretical) = s =
Standard deviation- Use theoretical formula to find s.Then find mean + s and mean – s.
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
Ex #5-- Theoretical formula Use the theoretical formula for s xi 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 Xi xi2
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. • …
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.
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
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
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
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 =