4.1 STATISTICAL MEASURES Statistical Measures allow us to compare

individual values to other values in a data set. They are things like:Per capitaPercent changePercentileWeighted mean

VOCABULARY Per Capita: means “for each head”, it

is the average per person Net Worth: Total assets (wealth) minus

total liabilities (debt) Percent Change: Measures a change

in value over time

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 h𝐶 𝑎𝑛𝑔𝑒=𝑛𝑒𝑤𝑣𝑎𝑙𝑢𝑒−𝑜𝑙𝑑 𝑣𝑎𝑙𝑢𝑒

𝑜𝑙𝑑𝑣𝑎𝑙𝑢𝑒×100

VOCABULARY CONT’D Percentile: A number between 1 and 99

indicating the percent of the population with a score less than or equal to a specific value

Percentile Rank: The percent of the population with a score less than a specific score

𝑝=( 𝐿+0.5𝐸𝑛 )×100

p: percentile RankL: the number of scores less than the particular scoreE: the number of scores equal to the particular scoren: total number of scores

VOCABULARY CONT’D Weighted Mean: A mean in which each

component has a different weighting factor; to calculate, multiply each value by its weighting factor, then divide by the sum of the factors

Let’s see if we can combine all this vocabulary and tackle a problem…

SAMPLE PROBLEM

Many business, health and economics statistics are expressed as per capita figures. In March 2008, the national wealth of Canada was $5 702 000 000 000. The national debt was $23 000 000 000. The population of Canada was 33 223 840.a) What was Canada’s per capita wealth?

Therefore, Canada’s per capita wealth is $171 623.75.

SAMPLE PROBLEM CONT’D

b) What was Canada’s per capita debt?

Therefore, Canada’s per capita debt is $692.27.

SAMPLE PROBLEM CONT’D

c) What was Canada’s per capita net worth?Method #1Per Capita Net Worth = Per Capita Wealth – Per Capita Debt = 171 623.75 – 692.27

= 170 931.48

Therefore Canada’s per capita net worth is $170 931.48.

Method #2

= $170 931.48

PERCENT CHANGERecall Percent Change: measures a change in value over time

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 h𝐶 𝑎𝑛𝑔𝑒=𝑛𝑒𝑤𝑣𝑎𝑙𝑢𝑒−𝑜𝑙𝑑 𝑣𝑎𝑙𝑢𝑒

𝑜𝑙𝑑𝑣𝑎𝑙𝑢𝑒×100

EX. 1: The table below shows a company’s profits each year for five years, as reported in a newspaper.

Year Profit ($)

2005 186000

2006 364000

2007 728000

2008 212000

2009 -22000

a) Calculate the percent change in profit from 2005 to 2006.

Therefore profits increased by 95.7% from 2005 to 2006.

PERCENT CHANGE CONT’Db) Calculate the percent change in profit from 2008 to 2009.

Year Profit ($)

2005 186000

2006 364000

2007 728000

2008 212000

2009 -22000

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 h𝐶 𝑎𝑛𝑔𝑒=𝑛𝑒𝑤𝑣𝑎𝑙𝑢𝑒−𝑜𝑙𝑑 𝑣𝑎𝑙𝑢𝑒

𝑜𝑙𝑑𝑣𝑎𝑙𝑢𝑒×100

Therefore profits decreased by 110.4% from 2008 to 2009.

c) The company’s financial report stated: “There was a 200% increase in profits from 2006 to 2007.” Do you agree with this statement?𝑃𝑒𝑟𝑐𝑒𝑛𝑡 h𝐶 𝑎𝑛𝑔𝑒=

𝑛𝑒𝑤𝑣𝑎𝑙𝑢𝑒−𝑜𝑙𝑑 𝑣𝑎𝑙𝑢𝑒𝑜𝑙𝑑𝑣𝑎𝑙𝑢𝑒

×100

Year Profit ($)

2005 186000

2006 364000

2007 728000

2008 212000

2009 -22000We disagree because the company’s profits only increased by 100%.

WEIGHTED MEAN WEIGHTED MEAN: A mean in which

each component has a different weighting factor; to calculate, multiply each value by its weighting factor, then divide by the sum of the factors.

WEIGHTED MEAN EXAMPLE

A college instructor uses a weighted mean to calculate her students’ marks. Hanna and David’s marks are shown, along with the weighting. Hanna David

Quiz (out of 30) 24 18

Assignment (out of 60) 40 46

Test (out of 120) 89 95

Independent Study (out of 60) 43 48

Performance Task (out of 100) 85 82

Final Exam (out of 90) 72 64WEIGHTING FACTORS

Q = quiz (15%)

A = assignment (15%)

T = test (25%)

IS = independent study (10%)

PT = performance task (10%)

EX = final exam (25%)

Who has the better percent overall mark and by how much?

1. Convert the scores to percents.

2. For each student, multiply each percent by the weight factor, find the sum of all the category weights, and then divide this sum by the sum of the weights.

Hanna David

Quiz (out of 30)

Assignment (out of 60)

Test (out of 120)

Independent Study (out of 60)

Performance Task (out of 100)

Final Exam (out of 90)

Hanna:

= 76.2%

David:

= 74.3%

Therefore, Hanna had the better overall mark by 1.8%.

WEIGHTING FACTORS

Q = quiz (15%)

A = assignment (15%)

T = test (25%)

IS = independent study (10%)

PT = performance task (10%)

EX = final exam (25%)

4.1 HOMEWORK p. 205 #1ace, 2bdf, 3, 4, 6, 9abcd