Centrality and spread

Lit review and method due next Wednesday. Bring copies for 3 peer reviewers.

Practice the summation notation.

Order of operations:

1. Parathesis
2. Exponents/Square roots
3. Multiple/Divide
4. Add/Subtract

All the statistics for our purposes is based on two concepts: centrality and spread.

Centrality: (aka Central tendency)

1. Mode (used for categorical data from nominal data or frequency data) - most frequently occuring value. (bi-modal, multi-modal, amodal - no mode, constant scores)
2. Median (used for ordinal data or ranked data) - know as 50th percentile or half the scores above and half below. For even number of cases, take the mean of the two middle scores.
3. Mean (used for scale data or equal interval data) - sum of scores / number of cases

Properties of the mean:

1. Sum of the deviation about the mean: sum of (x-mean) = 0
2. Square of sum of (x - mean) is a minimum. The actual mean will bring this equation to the lowest answer. If you substitute the mean with any other number, the equation will give you a greater answer.
3. Grand mean is not a mean of means. It is calculated based on weighting (due to sample size of each sample mean) Grand mean = (n1*mean1 + n2*mean1)/n1+n2