**Unit 3**

Topics:

**What is Central Tendency? **link:What is Central Tendency

- Learning Objectives

- Identify situations in which knowing the center of a distribution would be valuable
- Give three different ways the center of a distribution can be defined
- Describe how the balance is different for symmetric distributions than it is for asymmetric distributions.

**Measures of Central Tendency **link:Measures of Central Tendency

- Learning Objectives

- Compute mean
- Compute median
- Compute mode

**Median and Mean **link:Median and Mean

- Learning Objectives

- State when the mean and median are the same
- State whether it is the mean or median that minimizes the mean absolute deviation
- State whether it is the mean or median that minimizes the mean squared deviation
- State whether it is the mean or median that is the balance point on a balance scale

**Additional Measures of Central Tendency **link:Additional Measures

- Learning Objectives

- Compute the trimean
- Compute the geometric mean directly
- Compute the geometric mean using logs
- Use the geometric to compute annual portfolio returns
- Compute a trimmed mean

**Comparing Measures of Central Tendency **link:Comparing Measures

- Learning Objectives

- Understand how the difference between the mean and median is affected by skew
- State how the measures differ in symmetric distributions
- State which measure(s) should be used to describe the center of a skewed distribution

**Measures of Variability **link:Variability

- Learning Objectives

- Determine the relative variability of two distributions
- Compute the range
- Compute the inter-quartile range
- Compute the variance in the population
- Estimate the variance from a sample
- Compute the standard deviation from the variance

**Shapes of Distributions **link:shapes

- Learning Objectives

- Compute skew using two different formulas
- Compute kurtosis

**Effects of Linear Transformations **link:Effects of Linear Transformations

- Learning Objectives

- Define a linear transformation
- Compute the mean of a transformed variable
- Compute the variance of a transformed variable

**Variance Sum Law I **link:Variance Sum Law

- Learning Objectives

- Compute the variance of the sum of two uncorrelated variables
- Compute the variance of the difference between two uncorrelated variables

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