STAT 2507A – Week 2 - May 20

STAT 2507A – Week 2 - May 20 -...

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1 STAT 2507A – Week 2 –  May 20 Jerry Situ 4.1-4.5  Summery 2009
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Exercise from last week (1) 1) Income distribution is known to be right skewed. Which of the following  is true: a) Mean > Median > Mode b) Mode > Median > Mean c) Mean = Median = Mode 2) A sample of 6 persons is taken from the Canadian population. The age  of the people in the sample are: 23, 15, 99, 17, 4, 16. What is the  standard deviation. a) 32; b) 35; c) 1214 What is the median? a) 16; b) 16.5; c) 17 2
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Exercise from last week (2) 3) In community XYZ, houses have an average value of $200,000 with a  standard deviation $50,000. What proportion of houses exceed  $300,000? a) 2.5% b) 5% c) 95% d) At most 25% 4) Which measure of center is best to describe the relative frequency  histogram of income for the Canadian population. Assume the graph  looks as follows: a) Mean b) Median  c) Mode 3
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Calculating center and spread  from classes When you do not have the  individual data values, statistics  can only be estimated. Use midpoint as an estimate of  the average value of the  observations within the class. For example, we estimate 5  students have expenses of  $2500 each, 3 students have  expenses of $3500 each. Cannot do estimates when there  are open ended classes. 4 Distribution of student expenses 0 2 4 6 8 10 12 14 16 2000- 3000 3000- 4000 4000- 5000 5000- 6000 6000- 7000 7000- 8000 Number of students CLASS DEFINITION FREQUENCIES 2000-3000 5 3000-4000 3 4000-5000 15 5000-6000 16 6000-7000 8 7000-8000 3
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Calculating center and spread  from classes (2) 5 n x x n i i = = 1 N X N i i = = 1 μ Sample: Population: Data values available Mean n m f x j c j j = = 1 N m f c j j j = = 1 μ Sample: Population: Estimating with midpoints c is the number of  classes f is the frequency  count in the class. m is the midpoint of  the class ( 29 N X N i i = - = 1 2 2 μ σ ( 29 1 1 2 2 - - = = n x x s n i i Variance ( 29 N m f c j i = - = 1 2 2 μ σ ( 29 1 1 2 2 - - = = n x m f s c j i j 1 2 1 1 2 2 - - = = = n n x x s n i i n i i N N X X N i i N i i 2 1 1 2 2 - = = = σ 1 2 1 1 2 2 - - = = = n n fm m f s c j j c j j j N N m f fm c j j j c j j 2 1 1 2 2 - = = = σ
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Example 6 CLASS DEFINITION FREQUENCIES 2000-3000 5 3000-4000 3 4000-5000 15 5000-6000 16 6000-7000 8 7000-8000 3 Class Definition Frequencies (f j ) Midpoint (m j ) f j m j 2000-3000 5 2500 12500 3000-4000 3 3500 10500 4000-5000 15 4500 67500 5000-6000 16 5500 88000 6000-7000 8 6500 52000 7000-8000 3 7500 22500
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Role of probability Within Statistics: Used to describe the likelihood of getting a  particular sample
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