~2018-09-14

https://www.youtube.com/watch?v=8X2xfwBP4uo&list=PLIeGtxpvyG-KqNeLQVhw8yv9MI5dd0ky_

Population Segment

Impossible/impractical to measure the entire population.

2018-09-20

https://www.youtube.com/watch?v=vrWYw8d2830&list=PLIeGtxpvyG-K82r1fgL-DO1xKg133PXKh

categorial data - labels for exclusive categories quantitative data - numeric value of measure

frequency - count relative frequency - %

frequency distribution - frequency and relative frequency

DO NOTT USE - Pie and 3D charts; they are deceptive

https://www.youtube.com/watch?v=zC3GaPBJ4c4&list=PLIeGtxpvyG-K82r1fgL-DO1xKg133PXKh&index=2

histogram - no gab bar chart

• bins
• resolution
• distribution

try to find a sweet spot of bins_buckets_groups to show histogram distribution

type of histogram shapes

• left skew - more data on right (lighter in image histogram)
• right skew - more data on left (darker in image histogram)
• symmetric - kinda bell curve
• bimodal - bridge (2 humps)
• uniform - same everywhere
• no pattern

^ adjusting resolution (# of bins) can show different shapes.

https://www.youtube.com/watch?v=6L20ofJXZ7g&index=3&list=PLIeGtxpvyG-K82r1fgL-DO1xKg133PXKh

Stem & Leaf displays

shows

• rank order
• shape of distribution
• modal qualities - things that show frequency

data

50, 61, 66, 73, 82, 82, 90, 103, 108, 115

stem & leaf

 5 | 0
 6 | 1 6
 7 | 3
 8 | 2 2
 9 | 0
10 | 3 8
11 | 5

data doesn’t have to be in order but the stem and leaf does

Stretched stem and leaf

break up bins (not base 10); can repeat stem values

leaf is ALWAYS 1 digit for 2384 it would -> 23 | 8 (the 4 is lost)

Cross Tabulation

https://www.youtube.com/watch?v=e6pT-GyT0hk&index=4&list=PLIeGtxpvyG-K82r1fgL-DO1xKg133PXKh

compare two variables

usually done in pivot tables

standard deviation - variability from average

cross tabs are basis for Chi-square and ANOVA (advanced stats)

2018-09-21

https://www.youtube.com/watch?v=bUu5HIHIrRw&list=PLIeGtxpvyG-JMH5fGDWhtniyET88Mexcw

z-score

spread === variance === standard deviation === distribution

2018-09-26

https://www.youtube.com/watch?v=bUu5HIHIrRw&list=PLIeGtxpvyG-JMH5fGDWhtniyET88Mexcw

z-score distance from the mean

it ignores the actual unit

mean has a z-score === 0

z = (data point - mean) / standard deviation

score | mean | score - mean | z score |
----- | ---- | -----------: | ------: |
85    | 85   |            0 |       0 |
95    | 85   |           10 |    1.27 |
75    | 85   |          -10 |   -1.27 |
80    | 85   |           -5 |   -0.63 |
90    | 85   |            5 |    0.63 |

2018-09-27

https://www.youtube.com/watch?v=JIIXQaMXBVM&index=3&t=0s&list=PLIeGtxpvyG-JMH5fGDWhtniyET88Mexcw

Variance and Standard deviation

mean = (x bar) = x̄ variance = (sigma squared) = σ^2
standard deviation = (sigma) = σ n = total data points

σ = sqrt(sum(x-x̄)^2 / (n-1))

coefficient of variation

relative measure of variability

coefficient of variation = ( σ / x̄ ) * 100

helps compare data with different means

units don’t matter (comparing quality of the dataset not the measurements)

2018-10-01

https://www.youtube.com/watch?v=L5pgVbj3WwI&index=4&t=0s&list=PLIeGtxpvyG-JMH5fGDWhtniyET88Mexcw

watch him use excel stuff

2018-10-03

https://www.youtube.com/watch?v=5tLEDdDl5tw&index=5&t=0s&list=PLIeGtxpvyG-JMH5fGDWhtniyET88Mexcw

https://www.youtube.com/watch?v=5tLEDdDl5tw&index=5&t=0s&list=PLIeGtxpvyG-JMH5fGDWhtniyET88Mexcw

Normal distribution

look at data graphically first

look for:

• excess skew (lopsided)
• kurtosis (fat tails)
• bi-modal (two humps)
• have a non-standard distribution

he phrases this as “excess probability”

Graphical Tools

1. historgrams
2. stem and leaf plots
3. box plats (box and whisker plots)
4. P-P Plots
5. Q-Q Plots

https://www.youtube.com/watch?v=xGbpuFNR1ME&index=7&t=0s&list=PLIeGtxpvyG-JMH5fGDWhtniyET88Mexcw

Bivariate Relationships - Covariance

2 variables

covariance - how the variables change together

positive - both go up or down together - slope negative - inverse relation ship one up the other down - slope

covariance is direction only nothing about strength (that is correlation)

sample covariance

population covariance

https://www.youtube.com/watch?v=locZabK4Als&index=7&list=PLIeGtxpvyG-JMH5fGDWhtniyET88Mexcw

Covariance Matrix

R, SPSS, sass tools for summary data

Matrix / Scatter Plots

plots each variable agains each other variable

diagonal of covariance matrix is the variance of a variable with itself

excel uses the population covariance formal ( n vs n-1) fix by multiplying (n/n-1)

https://www.youtube.com/watch?v=4EXNedimDMs&list=PLIeGtxpvyG-JMH5fGDWhtniyET88Mexcw&index=8

Correlation

direction and strength of variance of 2 variables

correlation between -1 and +1 agnostic of units of data

correlation is standardized and covariance is not

correlation is only a linear relationship

correlation is NOT causations

strength is not statistically significance

r == Pearson correlation coefficient

covariance (x,y)/ (standard_deviation(x) * standard_deviation(y))

Rule of thumb:

• if |r| >= 2/sqrt(n) then relationship exists

2018-10-10

https://www.youtube.com/watch?v=qaFNhwNBY3k&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA

finite math

permutations vs combinations

probability is the count at which some event happens at a greater number of outcomes

we must be able to count in more complex ways to find certain probabilities

permutations - ordered list : number of different ways a certain number of objects can be arranged in order from a larger number of objects

n objects can be ordered in lists of size r

P(n,r)

combinations - groups (order doesn’t matter) : the number of diff ways that a certain number of objects as a group can be selected from a larger number of objects

n choose r

C(n,r)

10 horse race - top 3

Top 3 in any order C(10, 3) = 120 possibilities Top 3 in order P(10,3) = 720 possibilities

25 players in a 9 player lineup C(25,9) = 2,042,975 P(25,9) = 741,000,000,000

C(30,6) = 593,775 P(30,6) = 427,518,000

2018-10-13 10.22.25

https://youtu.be/6XWqDezwbaw

Combinations

Group order doesn’t matter

2018-10-15 08.11.39

https://www.youtube.com/watch?v=T1CjOkEb1ew&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA&index=3

Permutations

2018-10-16 09.24.56

https://www.youtube.com/watch?v=1oEQWo28w6U&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA&index=4

Combinations - Marble problem

marbles in a bag

• 4 red
• 3 blue
• 4 green
• 3 yellow

14 - total

How many sets of 4 are possible?

C(14,4) = 1001

How many sets of 4 are possible with 4 diff colors?

C(3,1) = blue C(4,1) = red C(4,1) = green C(3,1) = yellow

(3x4x4x3) = 144

How many sets of 4 are possible for at least 2 red?

2 red 2 not red C(4,2) = red C(10,2) = !red

= 270

or 3 red 1 not red C(4,3) = red C(10,1) = !red

= 40

4 red

C(4,4) = red

= 1

Combine above possibilities

270 + 40 + 1 = 311

How many sets of 4 are possible for none red but 1 green?

1 green and 3 other non-red non-green

C(4,1) = green C(6,3) = blue or yellow

= 4 x 20 = 80

2 green and 2 other blue or yellow

C(4,2) = green C(6,2) = blue or yellow

= 6 x 15 = 90

3 green and 1 other blue or yellow

C(4,3) = green C(6,1) = blue or yellow

= 4 x 6 = 24

4 green

C(4,4) = green

= 1

80 + 90 + 24 + 1 = 195

Reverse method

All possible without red or green (only blue or yellow) is C(6,4) = 15 All possible without red is C(10,4) = 210

Total minus - what we cannot have 210 - 15 = 195

2018-10-22 07.46.26

https://www.youtube.com/watch?v=VS1GQrt7s0I&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA&index=5

Dogs of the Dow

How many different 5-stock portfolios are possible?

10 choose 5 || C(10,5) = 252

How many diff stock portfolios contain GE & PG but not have INTC nor KFT?

PG & GE C(6,3) = 1x20 = 20

How many diff portfolios contain at least 4 stocks with yields >= 3.5%

C(6,4) + C(4,1) = 60 C(6,5) = 6 = 66

If we randomly choose 5 stocks what is the chance of our portfolio has 4 stocks with 3.5% yields

66/250 = 26.2%

2018-10-25

https://www.youtube.com/watch?v=NgLsfdEH4Go&index=6&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA

Combinations - Nearly Normal

n	r	expression	combinations
2	0	C(2,0)	1
2	1	C(2,1)	2
2	2	C(2,0)	1

as group size goes up (2,5,10,20) the histogram of all group sizes looks like normal curve

histogram -> discrete random variables normal curve -> continuous random variables

2018-10-31

https://www.youtube.com/watch?v=nxnZE1ZeqXw&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA&index=7

combinations under the curve

2018-11-05

https://www.youtube.com/watch?v=pcedp8eB4UQ&index=8&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA

Sets

Elements : individual things inside a set

N = Set N = {1,2,3,4,5,6,7,8,9}

4 ∈ N 4 is in set N

110 ∉ N 110 is not in set N

E⊆N E is a subset of N including equivalent set (subset of its twin)

E={2,4,6,8}

Proper subset E⊂N

E can be any subset of N, but E !== N

Empty set Z = {null} or Z = {}

empty set is a subset of any set

There are Infinite sets

2018-11-06

https://www.youtube.com/watch?v=V1J-4YFK7FQ&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA&index=9

Venn Diagrams

Unions

or is inclusive

A “union” B A∪B

Disjoint - no subset an empty set is a valid set

Universal set is all elements we are interested in; problem specific

There can be subsets in the universal set. Complement (A prime; A’) is the numbers in universal set but not in A

∩ = intersect A∩B (A intersect B)

2018-11-07

https://docs.google.com/spreadsheets/d/1zt0siGTvHhN7jK6_fj404lOwPekNsxXmBLyXDue6UpM/edit#gid=0

venn diagram region method

Ur (U sup r) Sf (S sup r)

compliment === not that region including empty

2018-11-08

https://www.youtube.com/watch?v=bycNlM4KnLQ&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA&index=11

cardinality of a union

number of elements in a set

prevent double counting

2018-11-10

[Finite Math: Venn Diagram Practice Problems - YouTube](https://www.youtube.com/watch?v=22tiyb7Kemk&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA&index=12)

2018-11-14

https://www.youtube.com/watch?v=DkHWKAy47X0&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA&index=13

Joint and Marginal Probabilities

2018-11-23

https://www.youtube.com/watch?v=4tyzC-MkzOY&list=PLIeGtxpvyG-I9m4otjYGCQL_1m0Edm0LA&index=14

2018-11-27

https://www.youtube.com/watch?v=rifK8BtHaYI&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX

random variables == R.V.

can be discrete or continuous

2018-11-28

https://www.youtube.com/watch?v=fGKd6ZtuTzM&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX&index=2

discrete random variables

can be infinite sequence (integers 1 to ♾)

whole units only no fractions of parts

2018-11-29

https://www.youtube.com/watch?v=XGM51WaHzNw&index=3&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX

discrete random variable probabilities

uniform probability distribution

probability is between 0 and 1 sum of all probabilities will add to 1

compound probabilities (add P(x) together)

2018-12-08

https://www.youtube.com/watch?v=u5svtXcKXEk&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX&index=4

expected value = average or mean of a random variable

2018-12-11

https://www.youtube.com/watch?v=lahWlKj9p7U&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX&index=5

discrete random variable variance

variable == how spread out from the mean

2018-12-13

https://www.youtube.com/watch?v=ConmIDAzRqI&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX&index=6

sales performance

quality control

2018-12-17

https://www.youtube.com/watch?v=nxKBfcwEulg&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX&index=7

Mean and Standard deviation

2018-12-19

https://www.youtube.com/watch?v=FwIguCYyu7o&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX&index=8

Sales Quota Performance

2018-12-20

https://www.youtube.com/watch?v=edf75Y0fIjA&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX&index=9

Binomial Distributions

2018-12-27

https://www.youtube.com/watch?v=sNP1w4z8HWQ&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX&index=10

binomial distribution

95% threshold (above is not due to random chance)

2018-12-28

poisson distributions queuing theory

2018-12-31

https://www.youtube.com/watch?v=833ciyKyKNw&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX&index=12

2019-01-02

https://www.youtube.com/watch?v=cKf4DPT0Xno&list=PLIeGtxpvyG-LWd2IOW1wveszJXy_aHytX&index=13