1. pencil, red pen, highlighter, GP notebook, graphing calculator
Have out:
M3M8D5
Bellwork:
Given the data set {3, 3, 5, 9}, determine the standard deviation by hand. Don’t use the “shortcut” on a calculator (but you may check your answer afterwards).

2. Recall the steps for standard deviation:
1) mean
2) difference between data and mean 4 2 3
3) square the differences
4) sum of the squares 1
5) average the squares
6) square roots the average (variance) 6 5

3. {3, 3, 5, 9} 4 2 3
= 5
+ 1 1 5 6
+ 1
+ 1
+ 2
+ 1
+ 1

4. 5–Number Summary and Box & Whisker Plots
Example #1: The following are scores on a math test:
55, 74, 83, 91, 78, 64, 81, 94, 74, 79, 80, 71
Rewrite the scores in ascending order:
_________________________________________________.
55, 64, 71, 74, 74, 78, 79, 80, 81, 83, 91, 94
Since there are 12 data points, the median is the average
between _____ th and _____ th points. 6 7
Median = ______
= 78.5

5. ___ ___ ___ / ___ ___ ___ / ___ ___ ___ / ___ ___ ___
The median is also called the ______ __________ because it is larger than ______% of the data.
50th
percentile 50 n
In general, the nth Percentile is larger than ____% of the data.
The entire data set can be split into four equal-sized groups
called ___________.
quartiles Q1
___, ___, and ___ are the dividing points between the ________. Q2 Q3
quartiles
___ ___ ___ / ___ ___ ___ / ___ ___ ___ / ___ ___ ___ 55 64 71 74 74 78 79 80 81 83 91 94 Q1 Q2 Q3
Q1 = _______
Q2 = _______
Q3 = _______
= 78.5 2
MEDIAN

6. ___ ___ ___ / ___ ___ ___ / ___ ___ ___ / ___ ___ ___
___ ___ ___ / ___ ___ ___ / ___ ___ ___ / ___ ___ ___ 55 64 71 74 74 78 79 80 81 83 91 94 Q1 Q2 Q3
Q1 = _______
Q2 = _______
Q3 = _______
= 72.5
= 78.5
= 82 2 2 2
MEDIAN 25
Q1 is the _____th Percentile. It is the median of the bottom half
of the data. In the example above, take the average between the
_____ rd and _____th points to determine Q1. 3 4 75
Q3 is the _____th Percentile. It is the median of the top half of
the data. In the example above, take the average between the
_____ th and _____th points to determine Q3. 9 10
Basically, compute the median (3 times).

7. For any data set, the 5–Number Summary is:
Write out the 5–Number Summary for the math scores.
______,
______
Min Q1
Med (Q2) Q3
Max 55
72.5
78.5 82 94

8. box
We use the 5–# Summary to make a ____ and ________ Plot.
whisker
______,
______
Min Q1
Med (Q2) Q3
Max 55
72.5
78.5 82 94
Step 1: Create a scale covering the smallest to largest values.
Step 2: Plot the data points from the 5–Number Summary above the line.
Step 3: Draw a rectangle beginning at Q1 and ending at Q3. Draw a line segment in the box representing Q2, the median.
Step 4: Draw whiskers from each quartile to the extreme value data points. Q1 Q2 Q3
min
max
Score 50 60 70 80 90
100

9. The “box” represents the middle _______ of the data. The
whiskers represent the ________ and ________ quartiles.
50%
upper
lower 3 3 Q1 Q2 Q3
min
3 tests
max
3 tests
Score 50 60 70 80 90
100
Notice that the box and whiskers are not equal in size. Why?
There are 3 tests in each quarter, so each quarter has the same amount of data. However, they are not spread out equally.
For example the range of tests in the first quartile is from 55 to 71.
However, the range of tests in the second quartile is from 74 to 78. The data is less spread out that the first quartile, hence, a smaller looking quartile.

10. Make a Box and Whisker Plot on a Calculator
While I’m pulling up my calculator on the computer, put the data for the previous problem in the L1 column.

11. Practice: Refer back to our ¼ mile times data (in seconds): {58, 102, 65, 70, 68, 75, 81, 84, 79, 68}.
Rewrite the times in ascending order: _______________________________________________.
58, 65, 68, 68, 70, 75, 79, 81, 84, 102
Find the 5–number summary. 58 68
72.5 81
102
______,
______
Min Q1
Med (Q2) Q3
Max
Make and label a box plot. 68
72.5 81 58
102 60 70 80 90
100
110

12. Interquartile Range spread
Recall that standard deviation is a measure of _________ about the ______.
Another measure of spread, which measures spread about the ________ is the _________________, the ________.
mean
median
interquartile range
IQR Q3 Q1
The IQR is defined as ____ - ____. For the ¼ mile times,
IQR = ____ - ____ = ____
The IQR is the width of the ______, the middle ______ of the data, for a box and whiskers plot. 81 68 13
box
50%

13. Make a box and whiskers plot on the calculator of the ¼ mile times.
STAT PLOT
1: PLOT 1… ON
ENTER ON
Select the second type. Arrow to the second box and hit
Make sure that “X list:” is L1 and “Freq:” is 1 as illustrated above.
ENTER
ZOOM
9: ZOOM STAT
Select
Since we chose the 2nd type of box, the outliers are not determined.
Select and use the left and right arrow keys to locate the 5–Number Summary.
TRACE

14. Select and use the left and right arrow keys to locate the 5–Number Summary.
TRACE 68
72.5 81 58
102
1st quartile
2nd quartile
3rd quartile
4th quartile 60 70 80 90
100
110
Note: there are the same number of points in each quartile, but the spread is variable
If a data point is more than __ standard deviations from X (mean), it is an outlier. There is also a way to determine outliers using the IQR. 2

15. 1.5 IQR Criterion
For the data in the previous problem, IQR = __ and 1.5 IQR = __
If a data point is ______ than 1.5 IQRs _______ Q3, it is an ______ outlier. 13
19.5
more
above
upper
Example #5: Find the cutoff for the upper outliers for this data. Fill in the data from the 5–number summary. 58 68
72.5
______,
______
Min Q1
Med (Q2) Q3
Max 81
102
Q3 = ____ Q IQR = _____ + _____ = _____ 81 81
19.5
100.5
102
Since student # 2 had a time of 102 seconds, and ____ > 100.5, 102 is an _______ _______.
upper
outlier
If a data point is ______ than 1.5 IQRs _______ Q1, it is a ______ outlier.
less
below
lower

16. Modified Box and Whiskers Plot
Example #6: Find the cutoff for the lower outliers for this data.
Q1 = ____ Q1 – 1.5 IQR = ______ – ______ = ______
Since there are no points below _________ seconds, there are ________ lower outliers. 68 68
19.5
48.5
48.5 no
Explanation…
Modified Box and Whiskers Plot
To modify the box and whiskers plot for outliers, we show outliers as _________, and only extend the whiskers as far as any data point that is ________ an outlier.
dots
not
To make a modified box and whiskers plot, do the following:
2nd
STAT PLOT
1: PLOT 1… ON
ENTER ON
Select the FIRST type, which shows the box and whisker plot with dots. Arrow to the FIRST box and hit
ENTER

17. 1.5(IQR)
1.5(IQR)
outliers
outliers
IQR Q1 Q3

18. Select and use the left and right arrow keys to locate the 5–Number Summary to help you make the box plot.
TRACE 68
72.5 81 58 84
102 60 70 80 90
100
110

19. Summary: Over the last several days, we have discussed three
measures of spread:
Range measures the spread from the minimum to the
maximum value.
Standard deviation measures spread of the data about the
_________.
mean
median
3. IQR measures spread about the __________.
(resistant to outliers)

20. Assignment # 5:
Day 5 Worksheet
DS 95 and 98

21. pencil, red pen, highlighter, GP notebook, graphing calculator
Have out:
4/20/11
Bellwork:
Given 2 data sets {3, 3, 5, 9} and {4, 5, 5, 10}, answer the following for each data set:
a) sketch a histogram.
b) find the average.
c) determine the standard deviation by hand. Don’t use the “shortcut” on a calculator (but you may check your answer afterwards).
d) which data set is more “spread out” from the mean?
total:

22. {3, 3, 5, 9} {4, 5, 5, 10} + 1 + 1 + 1 labeled axes + 1 bars +1 + 1
data
Frequency 3 4 5 6 1 2 7 8 9
+ 1
{3, 3, 5, 9}
+ 1
+ 1 labeled axes
+ 1 bars
data
Frequency 4 5 6 7 1 2 3 8 9 10
{4, 5, 5, 10} +1
+ 1
+ 1 labeled axes
+ 1 bars

23. Recall the steps for standard deviation:
1) mean
2) difference between data and mean 4 2 3
3) square the differences
4) sum of the squares 1
5) average the squares
6) square roots the average (variance) 6 5

24. {3, 3, 5, 9} 4 2 3 1
+ 2 5 6
+ 2
+ 1
+ 1

25. {4, 5, 5, 10} 4 2 3 1
+ 2 5 6
+ 2
+ 1
+ 1

26. data
Frequency 3 4 5 6 1 2 7 8 9
{3, 3, 5, 9}
The data from {3, 3, 5, 9} is more spread out from the mean.
+ 1
data
Frequency 4 5 6 7 1 2 3 8 9 10
{4, 5, 5, 10}
total:

27. b) Determine the 5–Number Summary and IQR. Show all work!
Practice: Answer the following using this data
{46, 41, 32, 27, 50, 38, 40, 29, 31, 47, 42, 30}
a) Rewrite the data in ascending order:
27, 29, 30, 31, 32, 38, 40, 41, 42, 46, 47, 50 Q1 Q2 Q3
b) Determine the 5–Number Summary and IQR. Show all work!
Q1 = _______
Q2 = _______
Q3 = _______
= 30.5
= 39
= 44 2 2 2
MEDIAN
______,
______
Min Q1
Med (Q2) Q3
Max 27
30.5 39 44 50

28. ______,
______
Min Q1
Med (Q2) Q3
Max 27
30.5 39 44 50 Q1 Q2 Q3
min
max 20 30 40 50