Notation: Md

The 50th percentile

The median is the middle score - the score at which half the scores are above and half the scores are below.

The median is

that point on the number line such that the sum of the distances of all scores in the group to that point is smaller than the sum of distances to any other point. If the median is substituted for every score in the group, less average error results than if the mean, mode, or any other value is used as a reference point… Glass & Hopkins, p. 58

Three types of samples:

  1. Samples with an odd number of untied scores. (The median is the middle score.)
  2. Samples with an even number of untied scores. (The median is the halfway between the two middle scores.)
  3. Samples with ties. For these, use the method below.

To find the median:

  1. Construct frequency distribution of the data
  2. How many observations are needed to reach 50%?
  3. Which “interval” contains the 50th percentile? (use cumulative frequency column; start at the bottom and go up until you meet or exceed the number of observations that represents 50%)
  4. Sketch a picture of the interval
  5. How far into the interval do you need to go? (Based on the number of observations within the interval in question, and based on the number of observations in the previous interval.)
  6. Where are you? Take lower limit of interval, add the number of observations it took to get to the median from the bottom interval, then divide by the total number of observations within the interval.

(You are looking for a number such that half of the observations fall below it and half the observations fall above it. In an ordered list, this would be halfway down (or up) the list.)

The three most common measures of central tendency are the mean, the median, and the mode.