ch. 3 – part 1 measures of central tendency measures of variation calculation standard deviation...
TRANSCRIPT
Ch. 3 – part 1•Measures of central tendency
•Measures of variation •Calculation standard deviation
Using the TI30XII
Notation- sample and populationsize Mean Variation Standard
deviationProportion
Sample n s
Population N p
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
Ex. #2: Find mean and medianSalary Frequency
10,000 1
20,000 4
30,000 3
250,000 1
Ex #3: GPAs – calculateClass Grade # credits
Math B (3.0) 4
English C (2.0) 2
Physics A (4.0) 5
Find the approximate mean, median, mode on these distributions
SymmetricUniform Bimodal
Skewed Left Skewed Right
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
How do they vary?-- RangeClass 1
100
90
70
50
40
Class 2
72
71
70
69
68
Measures of variation
• Range=
• Sample Standard deviation = s =
Basic formulassize Mean Variance Standard deviation
(algebraically equivalent)
Population
N
=
=
Sample
n
=
s2
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 1
100
90
70
50
40
Class 2
72
71
70
69
68
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 7Calculate the mean.
You should get 3
Ex #4-- Theoretical formula
Use the theoretical formula for s
xi 2
Ex # 4 -- Computation formula
Use the computational formula for s
Xi xi 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: 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 [2nd]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 X1=
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 again8. 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=).
10. Hit the [STATVAR] button.11. Use your right arrow to find the sample mean and sample standard deviation (sx=2.55)
12. 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 "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: 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
Calculate s, using shortcut formula xi xi
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.