Measures of Location/Central Tendency
When data is collected, from a common source, the individual values are likely to vary. It’s not easy to keep in mind all the values in a set of data hence it is essential to obtain a representative figure. Such a figure is known as a measure of central tendency or an average.
The Qualities of a good measure of central tendency includes:
- Should be rigidly defined to mean it should have same interpretation for different users
- Should be easy to interpret and understand based on all observations.
- Be suitable for further mathematical treatment
- Should not be affected much by extreme observations
- Should not be affected much by fluctuations of sampling
COMMON MEASURES OF CENTRAL TENDENCY
- Arithmetic mean
- Geometric mean
- Harmonic mean
- Median mean
- Mode mean
The Arithmetic mean of a given set of observation is their sum divided by the number of observations
Geometric mean is defined as the nth root of the product of items of a series. Geometric mean measures average change over a period of time.
Harmonic mean is an average mean of means. It is the reciprocal of the Arithmetic mean of the reciprocals of the values of items in a given series.
Median is a positional average. It is a value that occurs in the middle position of a set of data. To obtain median, arrange the data in ascending order. If the number of observations is:
Odd, median = (n+1/2)th item
Most frequently occurring value in a set of observation, when there is no frequently occurring value, then there is no mode. In a frequency distribution, mode is the value that corresponds to the highest frequency.