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

Notation- sample and population sizeMeanVariationStandard deviation Proportion Sample n s Population N  p

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 and median SalaryFrequency 10, , , ,0001

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

Find the approximate mean, median, mode on these distributions Symmetric UniformBimodal Skewed Left Skewed Right

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 = s =

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

Sample Standard deviation (s) formulas– theoretical and shortcut

The 2 s formulas are algebraically equivalent

Standard deviation- theoretical formula 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 #4-- Theoretical formula Use the theoretical formula for s x i 2

Ex # 4 -- Computation formula Use the computational formula for s X i x i 2

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

Example #6: 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: Calculate the mean. You should get

Calculate s, using shortcut formula x i x i Sum=740.9 sum=120, s = = = 50.7 Now, verify your work using the TI30XII.