Understanding Averages Dr. Kalman J. Andrassy

Scales of Measurement There are four scales (or levels) at which researchers measure. Nominal - categorical and naming variables that have no numerical value or set order. Examples include haircolor (blond, brown, black, etc.) or marital status (married, divorced, single, etc.). Ordinal – variables that do not have a set, individual numerical value but do have order to them. Examples include temperature rankings (hot, medium, cold), number ranges (0-9, 10-19, 20-29), or Likert values (strongly agree, agree, neutral, disagree, strongly disagree). Interval - variables with an equal interval but do not have an absolute zero and can go negative. Examples include degrees fahrenheit, degrees celsius, income (if you are losing money). Ratio - variables with an equal interval AND an absolute zero. Examples include weight (you cannot weigh -3 pounds), height (you cannot be -4 inches tall), degrees Kelvin (in which absolute zero is the complete absence of heat).

Measures of Central Tendency An Average is the single value that best represents a group of scores. It is the center value of all of the scores in a given group or “distribution” of scores. In statistics we call averages measures of central tendency (because they are those central values). Mean Median Mode

Mean The mean is the most frequently used average is the mean, which is the balance point in a distribution. Add up scores then divide by the # of scores. Used for variables at the interval or ratio levels of measurement.

Median The median, is the middle score in a distribution. Example: 1,2,3,4,5 Median= 3 The median is used instead of the mean when the distribution is highly skewed. Used for variables at the ordinal, interval or ratio levels of measurement

Mode The mode is the most frequently occurring score. EX: 1,2,3,3,4,5,6 The mode would be 3 here because it is the most occurring score. Used for variables at any level of measurement: nominal, ordinal, interval and ratio.