Sunday, 19 February 2017

Measures of Central Tendency

Measures of Central Tendency
Mean, Median, Mode and Range
When scores are tabulated into a frequency distribution, calculation of measures of central tendency (or central position) follows. Measures of central tendency can be better understood this way, for example, if we compress the entire distribution at one single point, then that single point represents the central tendency. Measures of central tendency are sometimes called measures of central location.
Score is the measurement of individual performance by means of tests. And when scores are expressed in equal units, they form an interval scale.
The value of a measure of central tendency serves two purposes. First, it is an “average” which represents all the scores. Second, it enables the researcher to compare two or more groups in terms of typical performance.
There are three “averages’ or “measures of central tendency” which are in common use. These are: (1) Mean, (2) Median, and (3) Mode.
Mean: It is an “arithmetic” mean. Mean is probably the most familiar average. The mean (of a set of scores) is the sum of separate scores (or measures) divided by their number.  It is used to describe the middle of a set of data.

Advantage of Mean:

1. Most popular measure. 
2. It is unique, there is only one answer.

Disadvantage of Mean:

1. It is affected by extreme values/scores.

Median: It is a “positional” average. When ungrouped scores (also known as raw data) are arranged in order of size, the median is the midpoint in the series. It is a measure of position rather than of magnitude.

Advantage of Median:

Extreme values do not affect the median as strongly as they affect the mean.

Disadvantage of Median:

It takes relatively long time to calculate for a very large set of data.
Mode: It is a “democratic” average. It is defined as the most frequently occurring score in a distribution. If there is only one value which occurs a maximum number of times, then the distribution is said to have one mode.

Advantage of Mode:

1. It is easy to understand and simple to calculate.
2. It is not affected by extreme large or small values.
3. It can be useful for qualitative data.

Disadvantage of Mode:

1. It is not used more frequently as compared to mean and median.
2. It is not necessarily unique; there may be more than one answer.
3. When no values repeat in the data set, the mode is every value and is useless.
4. When there is more than one mode, it is difficult to interpret and compare.