ch. 12 – part 1b
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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: - PowerPoint PPT PresentationTRANSCRIPT
Ch. 12 – part 1B•Measures of central tendency•Measures of variation •Shapes of distributions
•Calculation standard deviationUsing the TI30XII
Notation- sample and populationsize Mean Standard
deviation
Sample n s
Population N
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, median, modeSalary 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
Skewed distributions and measures of central tendency
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 (Theoretical)= s =
Standard deviation- Use theoretical formula to find s.
Then find mean + s and mean – s.
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 #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 xi 2
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: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. …
Directions continued7. 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
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 9967 62 45 89 76 43 9856 78 66 54 88 67 90
• Also, find mean + smean - 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 =