Mean is the arithmetic average of all the data values. Simply, it is the sum of all data values/number of data values
Median is the true center or the actual middle data value, when the data is arranged in ascending or descending order
Mode is the most frequent (often repeated data value)
It is easy to see that while all data must necessarily have a mean and a median, it does not necessarily have a mode. This is because, even in a huge database of say 1000 numbers, there might not be a single number repeated. This data has no mode, but has a mean value and a median value. A data set may have more than one mode. In this case, we say the data has multiple modes.
This is so far as ratio or interval scales of measurements are concerned. If a variable is measured on the ordinal scale (for example, rank order or the “bad, medium, good” type of data), arithmetic operations are not possible and therefore in this case, the “mean” may not be suitable.
(i) We use Mean as the appropriate measure of central tendency for interval measures such as the temperature in Celsius scale or Fahrenheit scale, and for ratio measures as in physical quantities, such as mass, length, energy, and temperature measured in K.
(ii) We use Median as the appropriate measure of central tendency for ordinal data such as the results of a horse race, which say only which horses arrived first, second, third, etc. but no time intervals are mentioned, and for interval measures such as the temperature in Celsius scale or Fahrenheit scale.
(iii) We use Mode as the appropriate measure of central tendency for nominal/categorical data such as gender, race, religious affiliation and birthplace.
AERD. (2014). Descriptive and Inferential Statistics. Retrieved from AERD
When estimating the mean, the arithmetic is not an exact measurement. The population shape only shows a frequency of values that is comparative to the entire population. Therefore, small samples do not measure the population in an accurate fashion. As the sample size grows larger than the numbers are more accurate. In this way the population shape is a concern when estimating a mean because if the shape is symmetrical, this is indicative of the mean being closer to the center of distribution. The more extreme the values become, the further away from the center the mean will become.
The sample size (n) will affect the accuracy of the estimated mean depending upon its size. The larger the sample, the more accurate the estimate. The smaller, the less accurate the estimate.
Sekaran, U. (2003). Research methods for business: A skill-building approach (4th ed.). New York, NY: John Wiley & Sons.