Graphing Data 4
- Lecture1.1
  
  Introduction
- Lecture1.2
  
  Basic Charts
- Lecture1.3
  
  Basic Charts Part 2
- Lecture1.4
  
  Randomness
Mean and Standard Deviation 5
- Lecture2.1
  
  Introduction
- Lecture2.2
  
  Random Walk
- Lecture2.3
  
  Random Walk Part 2
- Lecture2.4
  
  Mean and Standard Deviation
- Lecture2.5
  
  Mean and Standard Deviation Part 2
Distributions 6
- Lecture3.1
  
  Introduction
- Lecture3.2
  
  PDF and CDF
- Lecture3.3
  
  PDF and CDF Part 2
- Lecture3.4
  
  Z Scores
- Lecture3.5
  
  Plotting
- Lecture3.6
  
  Solution
Correlation and Linear Regression 7
- Lecture4.1
  
  Introduction
- Lecture4.2
  
  Basics
- Lecture4.3
  
  Correlation
- Lecture4.4
  
  Z-Score
- Lecture4.5
  
  Z-Score Part 2
- Lecture4.6
  
  Linear Regression
- Lecture4.7
  
  Linear Regression Part 2
Probability 3
- Lecture5.1
  
  Introduction
- Lecture5.2
  
  Probability Basics
- Lecture5.3
  
  Probability
Counting Principles 3
- Lecture6.1
  
  Introduction
- Lecture6.2
  
  Factorials and Permutations
- Lecture6.3
  
  Binomial Theorem
Binomial Distribution 3
- Lecture7.1
  
  Introduction
- Lecture7.2
  
  Binomial Distribution
- Lecture7.3
  
  Binomial Distribution Part 2
Confidence Interval 7
- Lecture8.1
  
  Introduction
- Lecture8.2
  
  Alpha
- Lecture8.3
  
  Confidence Intervals
- Lecture8.4
  
  Confidence Intervals Part 2
- Lecture8.5
  
  Confidence Intervals Part 3
- Lecture8.6
  
  Confidence Intervals Part 4
- Lecture8.7
  
  Confidence Intervals Part 5
Proportion Confidence Interval 3
- Lecture9.1
  
  Introduction
- Lecture9.2
  
  Equations
- Lecture9.3
  
  Solution
Hypothesis Testing 5
- Lecture10.1
  
  Introduction
- Lecture10.2
  
  The Null Hypothesis
- Lecture10.3
  
  The Null Hypothesis Part 2
- Lecture10.4
  
  One Tail Test
- Lecture10.5
  
  One Tail Test Part 2
Comparing Two Means 5
- Lecture11.1
  
  Introduction
- Lecture11.2
  
  Known Standard Deviations
- Lecture11.3
  
  Unknown Standard Deviations
- Lecture11.4
  
  Same Unknown Standard Deviations
- Lecture11.5
  
  Solution
Chi-squared Test 3
- Lecture12.1
  
  Introduction
- Lecture12.2
  
  Basics
- Lecture12.3
  
  Expected Values

Z-Score

One of the most common measures in statistics is the z-score. What it measures is how many standard deviations away from the mean a data point is.

Equation

$$z = \frac{x-\overline{x}}{\sigma}$$

First, let’s check out how far each point in our y data set is away from the mean.

xVals = list(range(100))
yVals = [x+randint(-20,20) for x in xVals]
xVals = np.array(xVals)
yVals = np.array(yVals)
print(yVals-yVals.mean())

Now, if we divide everything by the standard deviation…

print((yVals-yVals.mean())/yVals.std())

Now I want to introduce the correlation equation, there will be two versions, a standard one and a one using z-scores.

Equation

$$r_{xy} = \frac{\Sigma (x-\overline{x})(y-\overline{y})}{\sqrt{\Sigma (x-\overline{x})^2 \Sigma (y-\overline{y})^2}}$$

Challenge

Find the equation which uses z-scores

Prev Correlation

Next Z-Score Part 2

Basics

Graphing Data 4

Mean and Standard Deviation 5

Distributions 6

Correlation and Linear Regression 7

Probability 3

Counting Principles 3

Binomial Distribution 3

Confidence Interval 7

Proportion Confidence Interval 3

Hypothesis Testing 5

Comparing Two Means 5

Chi-squared Test 3

Z-Score

Equation

Equation

Challenge

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