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```					Measures of Central Tendency Mean Median Mode Midrange 22.23 21.45 22.14 29.47

Measures of Dispersion

Other Measures Sample Size Minimum Maximum First Quartile Third Quartile Given percentile = 75 4.62 54.31 15.94 27.04 90% Value of percentile =

32.922

Based on this output, I would say the typical bill is about \$21.45, noting that half of the bills are at least th

Measures of Dispersion Range Interquartile Range Standard Deviation Variance Coefficient of Variation 49.69 11.10 9.68 93.64 43.54% 31.90 50 41.58 73 51.25 74

Mean +/- 1 standard dev. 12.55 # Observations within 1 standard dev. Mean +/- 2 standard dev. 2.87 # Observations within 2 standard dev. Mean +/- 3 standard dev. -6.80 # Observations within 3 standard dev.

\$21.45, noting that half of the bills are at least that amount.

Measures of Central Tendency Mean Median Mode Midrange 3.55 3.40 4.10 3.65

Measures of Dispersion

Other Measures Sample Size Minimum Maximum First Quartile Third Quartile Given percentile = 75 0.50 6.80 2.60 4.30 90% Value of percentile =

5.3

Based on this output, I would say the typical tip is about \$3.40, noting that half of the customers tip at lea

Measures of Dispersion Range Interquartile Range Standard Deviation Variance Coefficient of Variation 6.30 1.70 1.32 1.74 37.15% 4.86 51 6.18 72 7.50 75

Mean +/- 1 standard dev. 2.23 # Observations within 1 standard dev. Mean +/- 2 standard dev. 0.91 # Observations within 2 standard dev. Mean +/- 3 standard dev. -0.41 # Observations within 3 standard dev.

\$3.40, noting that half of the customers tip at least that amount.

Measures of Central Tendency Mean Median Mode Midrange 2.59 2.00 2.00 3.00

Measures of Dispersion

Other Measures Sample Size Minimum Maximum First Quartile Third Quartile Given percentile = 75 1.00 5.00 2.00 3.00 90% Value of percentile =

4

Based on this output, I would say the typical size is 2 people per table, noting that it is the most common

Measures of Dispersion Range Interquartile Range Standard Deviation Variance Coefficient of Variation 4.00 1.00 0.92 0.84 35.44% 3.50 57 4.42 73 5.34 75

Mean +/- 1 standard dev. 1.67 # Observations within 1 standard dev. Mean +/- 2 standard dev. 0.75 # Observations within 2 standard dev. Mean +/- 3 standard dev. -0.16 # Observations within 3 standard dev.

ople per table, noting that it is the most common occurrence.

2a) For the typical bill, I would use the median since there are not likely any repetitions and the mean is e 2b) For the typical tip, I would use the median since there are not likely any repetitions and the mean is e 2c) For the typical size, I would use the mode since there will be a lot of repetitions across a few possible 3a) mean INCREASES 3b) median REMAINS THE SAME 3c) midrange INCREASES 3d) interquartile range REMAINS THE SAME 3e) standard deviation INCREASES 3f) range INCREASES 4) 3 * 2 * 4 * 5 =120 5) 3 * 5 * 4 = 60

y repetitions and the mean is easily distorted here. y repetitions and the mean is easily distorted here. petitions across a few possible party sizes.

Counting Techniques
number to choose from number to choose 10 4

Can I repeat myself? ----- if YES  ----- if NO  POWER Is order important? ----- if YES  ----- if NO  PERMUTATION COMBINATION
PERMUTATIONS COMBINATIONS 5,040 210 POWER 10,000

Counting Techniques
number to choose from number to choose 5 5

Can I repeat myself? ----- if YES  ----- if NO  POWER Is order important? ----- if YES  ----- if NO  PERMUTATION COMBINATION
PERMUTATIONS COMBINATIONS 120 1 POWER 3,125

Counting Techniques
number to choose from number to choose 15 10

Can I repeat myself? ----- if YES  ----- if NO  POWER Is order important? ----- if YES  ----- if NO  PERMUTATION COMBINATION
PERMUTATIONS COMBINATIONS 10,897,286,400 3,003 POWER 576,650,390,625

Counting Techniques
number to choose from number to choose 10 5

Can I repeat myself? ----- if YES  ----- if NO  POWER Is order important? ----- if YES  ----- if NO  PERMUTATION COMBINATION
PERMUTATIONS COMBINATIONS 30,240 252 POWER 100,000

Counting Techniques
number to choose from number to choose 20 5

Can I repeat myself? ----- if YES  ----- if NO  POWER Is order important? ----- if YES  ----- if NO  PERMUTATION COMBINATION
PERMUTATIONS COMBINATIONS 1,860,480 15,504 POWER 3,200,000

Counting Techniques
number to choose from number to choose 3 6

Can I repeat myself? ----- if YES  ----- if NO  POWER Is order important? ----- if YES  ----- if NO  PERMUTATION COMBINATION
PERMUTATIONS COMBINATIONS #NUM! #NUM! POWER 729

Counting Techniques
number to choose from number to choose 31 2

Can I repeat myself? ----- if YES  ----- if NO  POWER Is order important? ----- if YES  ----- if NO  PERMUTATION COMBINATION
PERMUTATIONS COMBINATIONS 930 465 POWER 961

Counting Techniques
number to choose from number to choose 26 2

Can I repeat myself? ----- if YES  ----- if NO  POWER Is order important? ----- if YES  ----- if NO  PERMUTATION COMBINATION
PERMUTATIONS COMBINATIONS 650 325 POWER 676

Probabilities Calculations Sample Space Gender Male Female Totals Simple Probabilities P(Male) P(Female) P() P(Accounting) P(Management) P(Finance) Joint Probabilities P(Male and Accounting) P(Male and Management) P(Male and Finance) P(Female and Accounting) P(Female and Management) P(Female and Finance) P( and Accounting) P( and Management) P( and Finance) Addition Rule P(Male or Accounting) P(Male or Management) P(Male or Finance) P(Female or Accounting) P(Female or Management) P(Female or Finance) P( or Accounting) P( or Management) P( or Finance) Major Accounting Management 100 150 100 50 200 200

Finance 50 50 100

Totals 300 200 0 500

60% 40% part a) prob = 40% or 200/500 0% 40% 40% 20%

part b) 200 accounting + 100 finance = 300 /

20% 30% 10% 20% 10% 10% 0% 0% 0%

80% 70% 70% 60% part c) prob = 60% or 300/500 70% 50% 40% 40% 20%

Conditional Probabilities P(Male given Accounting) 50% P(Male given Management) 75% P(Male given Finance) 50% P(Female given Accounting) 50% P(Female given Management) 25% P(Female given Finance) 50% P( given Accounting) 0% P( given Management) 0% P( given Finance) 0% P(Accounting given Male) 33% part d) prob = 33% or 100/300 P(Accounting given Female) 50% P(Accounting given ) #DIV/0!

P(Management given Male) P(Management given Female) P(Management given ) P(Finance given Male) P(Finance given Female) P(Finance given )

50% 25% #DIV/0! 17% 25% #DIV/0!

unting + 100 finance = 300 / 500 or 60%

Probabilities Calculations Sample Space Gas = Y Bank CC Bank = Y Bank = N Totals Simple Probabilities P(Bank = Y) P(Bank = N) P() P(Gas = Y) P(Gas = N) P() Joint Probabilities P(Bank = Y and Gas = Y) P(Bank = Y and Gas = N) P(Bank = Y and ) P(Bank = N and Gas = Y) P(Bank = N and Gas = N) P(Bank = N and ) P( and Gas = Y) P( and Gas = N) P( and ) Addition Rule P(Bank = Y or Gas = Y) P(Bank = Y or Gas = N) P(Bank = Y or ) P(Bank = N or Gas = Y) P(Bank = N or Gas = N) P(Bank = N or ) P( or Gas = Y) P( or Gas = N) P( or ) 60% part a) prob = 60% or 120/200 40% 0% 38% 63% part b) prob = 63% or 125/200 0% Gasoline CC Gas = N 60 60 15 65 75 125 0

Totals 120 80 0 200

30% part c) prob = 30% or 60/200 30% 0% 8% 33% 0% 0% 0% 0%

68% part d) prob = 68% or 135/200 93% 60% 70% 70% 40% 38% 63% 0%

Conditional Probabilities P(Bank = Y given Gas = Y) 80% P(Bank = Y given Gas = N) 48% part f) prob = 48% or 60/125 P(Bank = Y given ) #DIV/0! P(Bank = N given Gas = Y) 20% P(Bank = N given Gas = N) 52% P(Bank = N given ) #DIV/0! P( given Gas = Y) 0% P( given Gas = N) 0% P( given ) #DIV/0! P(Gas = Y given Bank = Y) 50% part e) prob = 50% or 60/120 P(Gas = Y given Bank = N) 19% P(Gas = Y given ) #DIV/0!

P(Gas = N given Bank = Y) P(Gas = N given Bank = N) P(Gas = N given ) P( given Bank = Y) P( given Bank = N) P( given )

50% 81% #DIV/0! 0% 0% #DIV/0!

Probabilities Calculations Sample Space Experience Satisfied Not Satisfied Totals Simple Probabilities P(Satisfied) P(Not Satisfied) P() P(On Time) P(Not On Time) P() Joint Probabilities P(Satisfied and On Time) P(Satisfied and Not On Time) P(Satisfied and ) P(Not Satisfied and On Time) P(Not Satisfied and Not On Time) P(Not Satisfied and ) P( and On Time) P( and Not On Time) P( and ) Addition Rule P(Satisfied or On Time) P(Satisfied or Not On Time) P(Satisfied or ) P(Not Satisfied or On Time) P(Not Satisfied or Not On Time) P(Not Satisfied or ) P( or On Time) P( or Not On Time) P( or ) Received Product On Time Not On Time 1197 33 127 143 1324 176 0

Totals 1230 270 0 1500

82% part a) prob = 82% or 1230/1500 18% 0% 88% part b) prob = 88% or 1324/1500 12% 0%

80% 2% part c) prob = 2% or 33/1500 0% 8% 10% 0% 0% 0% 0%

90% 92% 82% 98% 20% part d) prob = 20% or 303/1500 18% 88% 12% 0%

Conditional Probabilities P(Satisfied given On Time) 90% part f) prob = 90% or 1197/1324 P(Satisfied given Not On Time) 19% P(Satisfied given ) #DIV/0! P(Not Satisfied given On Time) 10% P(Not Satisfied given Not On Time) 81% P(Not Satisfied given ) #DIV/0! P( given On Time) 0% P( given Not On Time) 0% P( given ) #DIV/0! P(On Time given Satisfied) 97% part e) prob = 97% or 1197/1230 P(On Time given Not Satisfied) 47% P(On Time given ) #DIV/0!

P(Not On Time given Satisfied) 3% P(Not On Time given Not Satisfied) 53% P(Not On Time given ) #DIV/0! P( given Satisfied) 0% P( given Not Satisfied) 0% P( given ) #DIV/0!

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