One of the most important objectives of statistical analysis is to get one single value that describes the characteristics of the entire data.

**Statistical techniques
- Measures of central tendency**

One of the most important objectives
of statistical analysis is to get one single value that describes the characteristics
of the entire data. A common word used for measures of central tendency is average.
For example, if we collect the heights of
5000 students of a college, we will have 5000 figures. The persons mind is not capable
of registering all the data at a time. So we need a single figure which represents
the whole data. This single figure is known as average.

Since an average represents the entire
data, its value lies somewhere in between the two extremes i.e. the largest observation
and the smallest observation. For this reason the average is frequently referred
as measure of central tendency.

** **

Mean is defined as the value obtained
by dividing sum of values of all the given items by the number of items. It is also
called as arithmetic mean.

Mean = Sum of the values of all items
/ Total number of items

Mathematically it can be shown as

X=X_{1}+X_{2}+X_{3}+………….X_{N
}**/ N**

**X=** **∑**X/N

X=Menu

∑X = Sum of the Values of all items

N = Total number of items

**Example**

The following are the monthly
average temperature data of Cuddalore District. Find the mean annual temperature

Cuddalore

**Solution:**

**Formula:**

=∑X/N

= 25.3+26.58+28.46+30.61+31.32+30.75+30+29.34
+29.03+27.89+26.45+25.36/ 12

= 341.09 12

=28.42

**Answer:**

The Mean annual temperature of Cuddalore
district is 28.42

**Formula:**

** = A + ∑ fd/N × i**

**Where**

A = Assumed mean

f = frequency

i = class size

d = deviation from assumed mean

N = Total

d = [x – A] / i

Example

Calculate the mean for the following data of heights of the plants in a garden

Solution:

A = 25 , ∑ fd = 50 , N = 50, i = 10

**Formula:**

** **

Median is the middle value of a series
arranged in any order – ascending or descending. Median divides the series in to
two equal parts.

**Example **

The following are the monthly
minimum temperature of Chennai District. Find the median.

*Chennai*

**Solution:**

**Step
1:**

Arrange the data in Ascending Order

**Step
2:**

**Formula**

M = Value of the ([N+1]/2)^{th}
item

M = Value of the ([12 +1]/2)^{th}
item

M = Value of the (13/2)^{th}
item

M = Value of the 6.5 th item

M = (Size of 6^{th} item + size of 7 item)/2

M = (24.6+25.6) / 2.

**Answer**: M = 25.1

Calculate the median for
the following data

Literates by age in 2001

**Solution:**

**Calculation
of Median Class**

Class corresponding to 185.5 is 20-25 i.e. the Median Class

where

*I* = Lower limit of the median class

N = Total Numbers of frequeny

*f* = Frequeny of the median class

m = Cumulative frequency of the class
preceding the median class

c = The class interval of the median
class.

**Formula**

Median
= 20 + (0.03 × 5)

Median
= 20 + 0.15

**Answer:**** **Median = 20.15

** **

Mode is that value which occurs most
frequently in a set of observation or the item which repeats itself the greatest
number of times

Calculate mode for the following
data

Station: Cochin

From the data 25 is repeated 3
times. Hence the Mode is 25

**Answer: Mode =** 25

**Example
**

Calculate the mode for following
data

**Solution**

Highest Frequency = 15

Therefore 50 – 60 is the modal class

**Formula**

Modal class is the class which has maximum
frequency.

*f1* = frequency of the modal class

*f0* = frequency of the class preceding the
modal class

*f2* = frequency of the class succeeding
the modal class

*c*= width of the class limits

*I* = lower limit of mode interval

l = 50, f_{0} = 12, f_{1}
= 15, f_{2} = 12

**Answer:**** ****Mode = 55**

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12th Geography : Chapter 13 : Statistical Techniques : Statistical techniques - Measures of central tendency |

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