Measuring Numerical DataHOW MUCH??

• Absolute Quantities - ACTUAL• Relative Quantities - COMPARING

Types of Relative Quantities

• Percent or Fraction: used when comparing a part to whole of the same variable– Used to show relative change– Part/whole

• Rate: compare different types of variables (i.e. tickets per person, crimes per 1000 people)

• Ratio: compare same type of variable from two sources

Types of Relative Quantities

• Rates– Used to compare different types of variables – Examples

• Miles per hour• Tickets per person• Crimes per 1000 people

(HINT: What word is always in a statement using a rate?)

Example

Commmunity Area Total Number Living Population Below Poverty Line

Riverdale 9809 5487Oakland 6110 3178Washington Park 14146 7276Grand Boulevard 28006 12762North Lawndale 41768 18485Englewood 40222 17344Woodlawn 27086 10323Douglas 26470 9699West Garfield Park 23019 8161Near West Side 46419 16149East Garfield Park 20881 7179Fuller Park 3420 1174New City 51721 17687

Percent Of Formula

• Part = % Whole

• Whole means the entire pie.

• Part means one of the shaded regions or pieces of the pie.

3 Ways to Think about it

%whole

part

wholepart

%

partwhole *%

Percentage Change

• Percent Change Formula (find the percent) (New-Old)/Old = %

• Find new value (given old value and the percent change) Old*(1+%)=New

• Find old value (given new value and the percent change) Old = New

1 + %

Examples• The number of DVD players in homes in the United States

increased dramatically from 1999 to 2001, from 5.4 million to 25.1 million. By how many percent did it rise from 1999 to 2001?

• In 2001, there were 654 drive in theaters in the US, 77% fewer than in 1985. Approximately how many drive in theaters were there in 1985?

• Enrollment at DePaul University has grown by 36% from 1990 to 2001. If the Fall 1990 enrollment was 21,363 students then what was the total enrollment in 2001?

• A jacket was on sale for 40% off the original price of $79.99. I had an additional 15% off coupon for one item. What was the final price for the jacket?

Trendlines• Real World Data

– Most data is not perfectly linear– Trendlines (also known as line of best fit and least

squares line)– We can use the equation to make predictions

• Is it a good fit?• Extrapolation

– Predict the future– Constructing points between existing points is referred to as

interpolation

Least Square Regression Line Example

• y = mx + b• “Best Fit Line” aka “The least squares regression line”

The following table describes data for the number of people using a swimming pool over 8 days in summer and the corresponding maximum temperature (in degrees Celsius) on each day. a. Draw a scatterplot for this set of data.b. Trendline. Equation. R2c. Are we confident?

DayTemperature (Celcius) # of People

1 20 2802 24 3603 36 4504 32 4205 28 4006 38 5007 34 4758 26 320

Equation for Exponential Functions

• Like linear equations, there is also an equation for an exponential relationship

• y = P*(1+r)x

• P = a starting value (value of y when x=0)• r = percent change (written as a decimal)• x = input variable (usually time)

Change a number by percentage

y = P * (1 + r) (increase)y = P * (1 - r) (decrease)

– Y is the ending value– P is starting value and – r is percent change– Calculate in Excel

EXAMPLES

• The population of Jacksonville was 3,810 in 2007, and is growing at an annual rate of 3.5%. If this growth rate continues, what will be the approximate population in 2020?

• How can we solve this with an Excel spreadsheet?

• How can we solve this with an equation?

TYPES OF GRAPHS

• Pie Charts

Column Chart with more than one Series

X-Y Graphs (Line Graphs)

• Use X-Y graphs when you have a lot of data points

• The x-axis and the y axis has numerical data• This is also called a X-Y Scatter graph with a

straight line in Excel– Don’t use the “line graph” function in Excel

because it treats x-axis data as “categorical” and not numerical

• This causes the line not to come out right

X-Y Graphs (Line Graphs)

•Both variables (x and y) are numerical.• Connect the data points to create the line

Num

ber o

f Stu

dent

sFrequency of GPAs of Students in Math 101

Graph?

DePaul Majors in Five Subject Areas in 1999 and 2003 From the DePaul University Fact File

Area 1999 2003

Biology 244 310English 191 262International Studies 126 150Mathematics 49 54Political Science 253 406

GRAPH?Average Daily Temperature O'Hare Weather Station April 2003Temperatures in degrees Fahrenheit

Date Avg. Daily Temp (° F)

4/1/2003 604/2/2003 544/3/2003 424/4/2003 364/5/2003 294/6/2003 344/7/2003 324/8/2003 324/9/2003 36

4/10/2003 42

GRAPH?2000 Illinois Population by Race

Source: US Census

Racial CategoryPopulation (in thousands)

White Caucasian 9125

African American 1877

Other Single Race 723

Asian and Pacific Islander 429

Two or more Races 235

American Indian 31