[Statistics Tutorial 5] Measures of Central Tendency: Averages

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Measures of Central Tendency or The Measure of Location is a central or a representative value of statistical series.

When there is large raw data, it gets very difficult to understand or remember it. Therefore, we need a representative of the data that make it easy for us to determine the status of it.

E.g. It is very difficult to understand Income of millions of people in India. However, if it is said that the average income of people in India was Rs.25,000/- last year, it makes easier for us to guess the economic status of people in India.

We use the term “Average” in our day to day conversations. But what does it actually mean?

Average is a figure within the series of data that represents the data. Since this data is within the range of the series, it is sometimes called measure of central value.

Therefore, an average is a typical value around which other figures congregate.

 

Purposes and Functions of Averages:

1. To present the whole distribution of series into a representative figure.

2. For making comparisons easier (as it is easy to compare 2 numbers rather than 200)

 

Characteristics required for a good estimate:

1. Homogenous group (responses from participants should not vary too much as it gives an improper estimate of the “central value”.

2. Each case should be an approximate representative of the whole.

3. The more number of samples, the better would be the representativeness as it will depend less on predicting the behaviour of the population and more on getting its actual behavioural patterns and as more samples will ensure less extreme results which will in turn lead to better homogeneity.

 

There are 5 measures of averages namely:

1. Arithmetic Mean
2. Median
3. Mode
4. Geometric Mean
5. Harmonic Mean

 

Median & Mode are Positional averages that means they are not affected by distribution of the data (if there are very extreme scores) as they only calculate the position of the data or the frequency of occurrence of data and hence they can’t be used for further mathematical treatments.

 

Types of Averages

Different kinds of Averages

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