Measures of Center

• The average of all the values in the sample (population). We usually denote the mean of a sample by putting a bar on top of whichever letter we use to represent the sample: e.g., .
  • Mechanics
    1. X is the variable of interest.
    2. n is the sample size.
    3. are the actual sample values.
    Then the sample mean is

    

  • Notation:
    • Population mean: (``mu'').
    • Sample mean: (``X-bar'').
• The center point of the sample (population). More specifically, a number such that at least half of the values in a sample (population) are less than it and half of the values are greater than it. We often denote the median by putting a tilde on top of whichever letter we use to represent the sample: e.g., .
  • Mechanics:
    1. Order the data from smallest to largest.
    2. If n is odd, is the middle value.
    3. If n is even, is the average of the two middle values.
• The value which occurs most frequently in the sample (population). If the sample (population) has only one mode, it is called unimodal. If it has two modes, it is called bimodal; if it has more than two modes: multimodal. The mode is a good measure of central tendency only for a symmetric, unimodal sample (population).