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 –*

- Mathematical Averages (or Central Tendency)
- Positional Averages (or Central Tendency)

These two are further divided into

Mathematical Averages are divided into

**Arithmetic Mean (A.M.)****Geometric Mean (G.M.)****Harmonic Mean (H.M.)**

Positional Averages are divided into

**Median (M)****Mode (Z)****Partition Values**

Partition Values are further divided into –

**Quartiles****Quintiles****Deciles****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 –*

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

**Merits of Arithmetic Mean – **

- It is based on all items of the series.
- It is more reliable.
- Easy to calculate.

**Demerits of Arithmetic Mean – **

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

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