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 βfor each headβ, it
is the average per person Net Worth: Total assets (wealth) minus
total liabilities (debt) Percent Change: Measures a change
in value over time
πππππππ‘ hπΆ ππππ=πππ€π£πππ’πβπππ π£πππ’π
ππππ£πππ’πΓ100
VOCABULARY CONTβD 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
π=( πΏ+0.5πΈπ )Γ100
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 CONTβD 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
Letβs see if we can combine all this vocabulary and tackle a problemβ¦
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 Canadaβs per capita wealth?
Therefore, Canadaβs per capita wealth is $171 623.75.
SAMPLE PROBLEM CONTβD
b) What was Canadaβs per capita debt?
Therefore, Canadaβs per capita debt is $692.27.
SAMPLE PROBLEM CONTβD
c) What was Canadaβs per capita net worth?Method #1Per Capita Net Worth = Per Capita Wealth β Per Capita Debt = 171 623.75 β 692.27
= 170 931.48
Therefore Canadaβs per capita net worth is $170 931.48.
Method #2
= $170 931.48
PERCENT CHANGERecall Percent Change: measures a change in value over time
πππππππ‘ hπΆ ππππ=πππ€π£πππ’πβπππ π£πππ’π
ππππ£πππ’πΓ100
EX. 1: The table below shows a companyβs profits each year for five years, as reported in a newspaper.
Year Profit ($)
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 CONTβDb) Calculate the percent change in profit from 2008 to 2009.
Year Profit ($)
2005 186000
2006 364000
2007 728000
2008 212000
2009 -22000
πππππππ‘ hπΆ ππππ=πππ€π£πππ’πβπππ π£πππ’π
ππππ£πππ’πΓ100
Therefore profits decreased by 110.4% from 2008 to 2009.
c) The companyβs financial report stated: βThere was a 200% increase in profits from 2006 to 2007.β Do you agree with this statement?πππππππ‘ hπΆ ππππ=
πππ€π£πππ’πβπππ π£πππ’πππππ£πππ’π
Γ100
Year Profit ($)
2005 186000
2006 364000
2007 728000
2008 212000
2009 -22000We disagree because the companyβs 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 studentsβ marks. Hanna and Davidβs 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