Statistics

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.

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

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.

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

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.

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.

  

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.

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

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

356Divide by the number of tests. 5Your average is 71

Use the Pen in the Lower Left Corner to answer this question.

What is the average of these numbers?

567432902693356996

Use the Pen in the Lower Left Corner to answer this question.

What is the average of these numbers?

6543734329062

6119336956

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.

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.

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.

Finding the Mean in Excel

Type the numbers intothe cells.

Highlight the cells youwish to average.

Click the auto sum button.

Click on Average.

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.

Find the Average of these Numbers Using Excel

456675844345975

1,3573,4527,6538,0093,4455,679

3,464 56720,03

456

376543

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?

Income of Members in a Neighborhood

Neighbor Income Neighbor Income1 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 happento the average if a person moves in who makes $20,000,000.

16 20,000,000

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 84Rewrite the numbers in order below and circle the median.

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 666Rewrite 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.

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.

Be Careful!

The numbers in the Number box should match the correct cells.

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.

Find these Ranges456675844345975

1,3573,4527,6538,0093,4455,679

3,464 56720,03

456

376543

Use the Pen in the Lower Left Corner to answer this question. You may use a calculator.

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

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.

Combine all Three

You can highlightyour work, and rightclick and copy. Go to your paper and right click and paste.

Frequency Table

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

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 ofNeighbors

Complete the Frequency Table.

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.

Income Number ofNeighbors

Fraction Predictor Number

5,000 1 1/1610,000 315,000 320,000 525,000 130,000 220,000,000 1

Use the calculator.

one dividedby 16 equals

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.

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

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

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

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

Create a Frequency Chart of the Following Information

Student GradesJack 82Jill 89Goldilocks 75Cinderella 100Peter Piper 100Hansel 82Gretel 75Puss in Boots 75

Grades Range Frequency

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

Online Challenge

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