Statistics – Measures of Central Tendency – Arithmetic Mean

What is the Measure of Central Tendency ?

Measure of Central Tendency can be defined as a single value that represents the whole set of observation of data, this single value lies somewhere within the range of data, that’s why it is called Measure of Central Tendency.

Types of Measures of Central Tendency –

1. Mathematical Averages (or Central Tendency)
2. Positional Averages (or Central Tendency)

These two are further divided into

Mathematical Averages are divided into

1. Arithmetic Mean (A.M.)
2. Geometric Mean (G.M.)
3. Harmonic Mean (H.M.)

Positional Averages are divided into

1. Median (M)
2. Mode (Z)
3. Partition Values

Partition Values are further divided into –

1. Quartiles
2. Quintiles
3. Deciles
4. Percentiles

Arithmetic Mean –

Arithmetic mean is the value we gets by dividing the sum of observations by the no. of observations. It is denoted by

For example – We have given observations as, 5, 35, 12, 21, 3, 8, We have to find A.M.

So we will add all the given observations, SUM = 5+35+12+21+3+8=84

No. of observations are 6, as we can count, so A.M. will be 84/6 = 14

Arithmetic Mean has three types of series,

1. Individual Series – It has two methods

Direct Method –

Assumed Mean Method –

2. Discrete Series – It also has two methods

Direct Method –

Assumed Mean Method –

3. Continuous Series – It has three methods

Direct Method –

Assumed Mean Method –

Step Deviation Method –

Combined Arithmetic Mean – Combined Arithmetic Mean is used when we have to find the Mean of two or more arithmetic series.

Weighted Arithmetic Mean – Weighted Arithmetic Mean gives equal importance to each item of the series.

Properties of Arithmetic Mean –

1. It is a mathematical average.
2. If all the numbers are replaced by some number, even then mean won’t change.
3. If we add/subtract/multiply/divide all the items with a number, then the mean will be changed by the same number.
4. It can be shown on graph.
5. Sum of deviations of all items from the mean is zero.
6. Sum of squared deviations from the mean is minimum.

Merits of Arithmetic Mean –

1. It is based on all items of the series.
2. It is more reliable.
3. Easy to calculate.

Demerits of Arithmetic Mean –

1. It is affected by the extreme values.
2. Sampling fluctuations may not provide the correct value.
3. It is difficult to plot on graph.