1. Click the mouse button or press the Space Bar to display the answers.
5-Minute Check on Activity 7-8
What type of an experiment is it when neither the patient nor the doctor knows what type of pill is being given?
List the three major components of any experimental design
A “sugar pill” is also known as a ________________.
What is the only thing that can establish cause and effect?
What do we call a group in the experiment which treatments are measured against?
Double-blind experiment
Randomization, replication, and control
Placebo
Well designed experiment
Control group
Click the mouse button or press the Space Bar to display the answers.

2. Activity 7 - 9 A Switch Decision
Submarine interior (unspecified class) at the Royal Naval Museum, Copenhagen, Denmark
Activity 7 - 9
A Switch Decision

3. Objectives
Measure the variability of a frequency distribution

4. Vocabulary
Standard Deviation – measures how much the data deviates from the mean
Boxplot – statistical graph that helps visualize the variability of a distribution
Five-number Summary – the min, quartile 1, 2 and 3 and the max of the data set

5. Activity
The following sets of data are the result of testing two different switches that can be used in the life-support system on a submarine. Two hundred of each type of switch were placed under continuous stress until they failed, the recorded in hours. Switch A and B have approximately the same means and medians, as displayed by the following histograms.

6. Activity cont
1. What does the means and medians being the same tell us about the distributions?
Distributions are symmetric

7. Activity cont 2. Which distribution is most spread out?
Switch B is more spread out

8. Activity cont
3. Which distribution is packed more closely together around its center?)
Switch A is tighter

9. Activity cont 4. Which of these two switches would you choose and why?
Switch A because is varies less

10. Activity cont 5. Determine the range of the two switches:
Switch A: – = 10.84
Switch B: – = 28.16

11. Activity cont
6. Determine the IQR (interquartile range), which is Q3 – Q1 for each switch
Switch A: – = 2.94
Switch B: – = 6.46

12. Activity cont
7. Write down sx for each switch (this is something we will call the standard deviation)
Switch A: Switch B: 5.00

13. Measures of Spread
Variability is the key to Statistics. Without variability, there would be no need for the subject.
When describing data, never rely on center alone.
Measures of Spread:
Range - {rarely used ... why?}
Quartiles - InterQuartile Range {IQR=Q3-Q1}
Variance and Standard Deviation {var and sx}
Like Measures of Center, you must choose the most appropriate measure of spread.

14. Standard Deviation
Another common measure of spread is the Standard Deviation: a measure of the “average” deviation of all observations from the mean.
To calculate Standard Deviation:
Calculate the mean.
Determine each observation’s deviation (x - xbar).
“Average” the squared-deviations by dividing the total squared deviation by (n-1).
This quantity is the Variance.
Square root the result to determine the Standard Deviation.

15. Standard Deviation Properties
s measures spread about the mean and should be used only when the mean is used as the measure of center
s = 0 only when there is no spread/variability. This happens only when all observations have the same value. Otherwise, s > 0. As the observations become more spread out about their mean, s gets larger
s, like the mean x-bar, is not resistant. A few outliers can make s very large

16. Standard Deviation Variance: Standard Deviation:
Example 1.16 (p.85 of YMS): Metabolic Rates
1792
1666
1362
1614
1460
1867
1439

17. Total Squared Deviation
Standard Deviation
1792
1666
1362
1614
1460
1867
1439
Metabolic Rates: mean=1600 x
(x - x)
(x - x)2
1792
192
36864
1666 66
4356
1362
-238
56644
1614 14
196
1460
-140
19600
1867
267
71289
1439
-161
25921
Totals:
214870
Total Squared Deviation
214870
Variance
var=214870/6
var=
Standard Deviation
s=√
s= cal
What does this value, s, mean?

18. Example 1 Which of the following measures of spread are resistant?
Range
Variance
Standard Deviation
Not Resistant
Not Resistant
Not Resistant

19. Standard Deviation Using the TI-83
Enter the test data into List, L1
STAT, EDIT enter data into L1
Calculate Standard Deviation
Hit STAT go over to CALC and select 1-Var Stats and hit 2nd 1 (L1)
Read sx to get standard deviation
Square sx to get variance
x is population standard deviation (and won’t be used by AFDA)
Don’t worry about the formula we just went over

20. Example 2
Given the following set of data: What is the range? What is the standard deviation? What is the variance? 19 22 23 26 27 28 29 30 31 32
= 13
3.751
(3.751)2 =

21. Quartiles Quartiles Q1 and Q3 represent the 25th and 75th percentiles.
To find them, order data from min to max.
Determine the median - average if necessary.
The first quartile is the middle of the ‘bottom half’.
The third quartile is the middle of the ‘top half’. 19 22 23 26 27 28 29 30 31 32
Q1=23
med
Q3=29.5 45 68 74 75 76 82 91 93 98
med=79 Q1 Q3

22. 5-Number Summary, Boxplots
The 5 Number Summary provides a reasonably complete description of the center and spread of distribution
We can visualize the 5 Number Summary with a boxplot.
MIN Q1
MED Q3
MAX
min=45
Q1=74
med=79
Q3=91
max=98
Outlier? 45 50 55 60 65 70 75 80 85 90 95
100
Quiz Scores

23. Box Plots Using the TI-83 Enter the test data into List, L1
STAT, EDIT enter data into L1
Calculate 5 Number Summary
Hit STAT go over to CALC and select 1-Var Stats and hit 2nd 1 (L1)
Use 2nd Y= (STAT PLOT) to graph the box plot
Turn plot1 ON
Select BOX PLOT (4th option, first in second row)
Xlist: L1
Freq: 1
Hit ZOOM 9:ZoomStat to graph the box plot
Copy graph with appropriate labels and titles

24. Determining Outliers “1.5 • IQR Rule”
InterQuartile Range “IQR”: Distance between Q1 and Q3. Resistant measure of spread...only measures middle 50% of data.
IQR = Q3 - Q1 {width of the “box” in a boxplot}
1.5 IQR Rule: If an observation falls more than 1.5 IQRs above Q3 or below Q1, it is an outlier.
Why 1.5? According to John Tukey, 1 IQR seemed like too little and 2 IQRs seemed like too much...

25. Outliers: 1.5 • IQR Rule To determine outliers: Find 5 Number Summary
Determine IQR (Q3 – Q1)
Multiply 1.5xIQR
Set up “fences”
Lower Fence: Q1-(1.5∙IQR)
Upper Fence: Q3+(1.5∙IQR)
Observations “outside” the fences are outliers.

26. Outlier Example } { 10 20 30 40 50 60 70 80 90 100 Spending ($)10 20 30 40 50 60 70 80 90
100
Spending ($)
IQR=
IQR=26.66
1.5IQR=1.5(26.66)
1.5IQR=39.99 }
fence:
= 85.71
fence: = {
outliers

27. Example 3
Consumer Reports did a study of ice cream bars (sigh, only vanilla flavored) in their August 1989 issue. Twenty-seven bars having a taste-test rating of at least “fair” were listed, and calories per bar was included. Calories vary quite a bit partly because bars are not of uniform size. Just how many calories should an ice cream bar contain? Construct a boxplot for the data above.
342
377
319
353
295
234
294
286
182
310
439
111
201
197
209
147
190
151
131

28. Example 3 - Answer
Q1 = 182 Q2 = Q3 = 319 Min = 111 Max = 439 Range = 328 IQR = 137 UF = LF = -23.5
Calories

29. Example 4
The weights of 20 randomly selected juniors at MSHS are recorded below: a) Construct a boxplot of the data b) Determine if there are any outliers c) Comment on the distribution
121
126
130
132
143
137
141
144
148
205
125
128
131
133
135
139
147
153
213

30. Example 4 - Answer
Q1 = Q2 = 138 Q3 = Min = 121 Max = 213 Range = 92 IQR = 15 UF = 168 LF = 108 Mean = StDev = 23.91
Extreme Outliers ( > 3 IQR from Q3) * *
Weight (lbs)
Shape: somewhat symmetric Outliers: 2 extreme outliers
Center: Median = Spread: IQR = 15

31. Summary and Homework Summary Homework
Variability of a frequency distribution refers to how spread out the data is, away from center
Range is the max – the min of the data
Deviation of a data value is how far away from the mean it is
Standard deviation is a measure of how spread out all of the data is
Boxplot is a graph of the 5-number summary
Homework
pg 861 – 863; problems 1, 4, 6, 7