Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”)

1. Statistics

2. Statistics are pieces of data that are gathered
and analyzed to provide information that
can have an impact on our lives.
On the following pages is a historical story
showing how the use of statistics can make
a difference.

3. It was the year 1840.
The place was
London, England.

4. Thousands of people in the cities were dying of a
mysterious disease called cholera. There was no
known cure and no one knew what caused the
disease. What was especially frustrating was that it
was unclear why people contracted the disease
while others did not.

5. Doctor John Snow, a
London doctor,
decided to place dots
on a map of London to
represent each cholera
death.

6. He found out that there
was a connection
between the cholera
deaths and one water
pump on Broad Street
in London. It became
very clear that
something was
contaminating the
water at this pump and
killing thousands of
people.

7. Dr. Snow’s use of statistics led to changes
that saved thousands of lives. After the
lesson, you will create a study you can do at
our school to help solve a problem. Be sure
to name the study, describe the study,
explain how you intend to avoid bias, and
how you will display your results.

9. Data
• Data is the information that is collected.
• Dr. Snow placed a dot on a map of London
showing everywhere someone in the city
died of cholera. That was the data.

10. Mean
The mean is another word for average. The
average is the sum of all measurements
divided by the number of observations in
the data set.
89 100 78 0 89

11. If these were your grades on science tests,
what would your grade be? You would
need to find the average.
Add the numbers.
89 100 78 0 89
356
Divide by the number of tests. 5
Your average is 71

12. Use the Pen in the Lower Left Corner to answer this question.
What is the average of these numbers?
567
432
902
693
356
996

13. Use the Pen in the Lower Left Corner to answer this question.
What is the average of these numbers?
65437
3432
9062
61193
36956

14. Using a Calculator to Find Average
Insert each number followed by a
plus sign.
Touch the equal sign.
Touch the divide sign.
Touch the number of items you added.
Touch the equal sign.

15. Get the Calculator in Accessories
• Click the Start button.
• Click Programs.
• Click Accessories.
• Click Accessories.
• Grab the blue bar at the top of the calculator
and move it where it is most useful.

16. Open the Excel Program
• Click Esc.
• Click the Start Button.
• Click Programs.
• Click Microsoft Office.
• Click Excel.
• Click the Restore Down button.
• Click on this Powerpoint.
• Click the Restore Down button.
• Arrange the two programs side by side.

18. Finding the Mean in Excel
Type the numbers into
the cells.
Highlight the cells you
wish to average.
Click the auto sum button.
Click on Average.

19. Number in a Sequence
• What is the average of these three numbers?
33 34 35
If you have a set of odd numbers in a series,
the average is the middle number.

20. Find the Average of these Numbers
Using Excel
456
675
844
345
975
1,357
3,452
7,653
8,009
3,445
5,679
3,464
567
20,03
4
56
376
543

21. Bowling Averages
• Suppose you bowled three games. Your
scores were 130, 140 and 150. What would
your average be?
• How about 145, 155, and 180?

22. Income of Members in a Neighborhood
Neighbor Income Neighbor Income
1 10,000 9 15,000
2 5,000 10 20,000
3 15,000 11 15,000
4 10,000 12 30,000
5 20,000 13 30,000
6 25,000 14 20,000
7 10,000 15 20,000
8 20,000
What is the average income? What would happen
to the average if a person moves in who makes $20,000,000.
16 20,000,000

23. Median
The median of a set of data is the number in
the middle. To find the median, we need to
line up all the data from lowest to highest
and then take the middle number.
67 34 85 33 84
Rewrite the numbers in order below and circle the median.

24. If the list of data is an even number, then there will
not be a middle number to use for the median. In that
case, take the middle two numbers and average them.
657 534 239 554 935 666
Rewrite the numbers in order from lowest to highest.
Average the two middle numbers to find the median.
Use the Pen in the Lower Left Corner to answer this question.

25. Finding the Median in Excel
• Go to Excel.
• Type in Your numbers.
• Click the Auto Sum icon.
• Click on More Functions.
• Click on “Or select a category”.
• Select Statistical.
• Scroll down and select Median.

26. Be Careful!
The
numbers
in the
Number
box
should
match the
correct
cells.

27. Range
Another measure that is helpful when we
analyze data is the range. The range is the
difference between the lowest and highest
number in the set.
If the range is large, it warns you that you
will probably won’t get useful data from the
average.

28. Find these Ranges
456
675
844
345
975
1,357
3,452
7,653
8,009
3,445
5,679
3,464
567
20,03
4
56
376
543
Use the Pen in the Lower Left Corner to answer this question. You may use a calculator.

29. Mode
The mode in a set of data is the number that
occurs the most.
Find the mode of these numbers.
54 100 95 100 90 75 100 85 95
25 10 10 25 5 10 25 10 5

30. Finding Mode in Excel
• Open Excel.
• Type numbers in the cells.
• Highlight the cells and click the AutoSum
icon.
• Select Mode.
• If there is no mode, N/A will appear.

31. Combine all Three
You can highlight
your work, and right
click and copy. Go to
your paper and right
click and paste.

32. Frequency Table
A frequency table is a table indicating how
many of each number is in the set.

33. Neighbor Income Neighbor Income
1 10,000 9 15,000
2 5,000 10 20,000
3 15,000 11 15,000
4 10,000 12 30,000
5 20,000 13 30,000
6 25,000 14 20,000
7 10,000 15 20,000
8 20,000 16 20,000,000
Income Number of
Neighbors
Complete the Frequency Table.

34. Relative Frequency
The relative frequency helps you to make
predictions. To find predictor numbers, use
the frequency table . Make a fraction
comparing the number compared to the total
number. Then change the fraction into a
decimal.

35. Income Number of
Neighbors
Fraction Predictor
Number
5,000 1 1/16
10,000 3
15,000 3
20,000 5
25,000 1
30,000 2
20,000,000 1
Use the calculator.
one divided
by 16
equals

36. Summary
When we collect data and interpret it, we can
make important decisions that can have a
profound impact on our lives. Think of the
dramatic effect that collecting data can have
on our lives.

37. You may look back at the lesson if you need help.

38. Using Your Math Skills Solve the
Following Problem.
What is the mean, median, and mode of these numbers? Show work.
John went bowling. He bowled five games. His scores were
154, 165, 125, 165, and 190.
Mean/Average Median
Mode

39. Do this Problem on the Calculator.
• Find the mean, median, and mode of the
following numbers:
5764, 2345, 8456, 5764, 2234, 9010, 5437
Mean Median
Mode

40. Do this Problem in Excel.
Find the mean, median, and mode of the following numbers.
Then highlight your work in Excel, copy and paste on this
page.
456, 654, 456, 456, 654, 345, 324, 765, 876, 987, 678, 567, 934

41. Create a Frequency Chart of the
Following Information
Student Grades
Jack 82
Jill 89
Goldilocks 75
Cinderella 100
Peter Piper 100
Hansel 82
Gretel 75
Puss in Boots 75
Grades Range Frequency

42. Determine the Relative Frequency.
You may use a calculator.
Allowance Frequency Fraction Predictor
Number
$0-$5.00 8
$5.01-$10.00 9
$10.01-
$15.00
3

43. Online Challenge
Try playing the Landmark shark game for
more practice with range, median, and
mode:
http://media.emgames.com/emgames/de
mosite/playdemo.html?
activity=M5A006&activitytype=dcr&leve
l=3
(Requires ShockWave Player)