# Analysis of Data

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In statistical enquiry, the first step is to gather the facts through various methods. Gathered facts are edited, classified as per similarities in data, tabulated based on commonality in variables and finally represented in the form of diagrams and graphs.

After gathering of data, Analysis of data is done. Analysis of data is a technique through which significant facts are derived from the numerical data. First step in data analysis is the conversion of raw data into frequency distribution tables. Then we derive a single value, which represents entire data. That single value is called Central Tendency.

Central Tendency: Tendency of data to cluster towards the central location or value is called central tendency.

Purpose and functions of Central Tendency Value:

To convert the collected information and raw data in brief.

To facilitate comparison between two or more groups.

To present a representative value from raw data.

To facilitate future policy and programme.

Central Tendency of data can be derived in different ways. There are three major methods

Arithmetic Mean

Median

Mode

Arithmetic Mean: It is also known as Average. Arithmetic mean can be obtained by dividing the sum of all items by the number of items.

Where, x= item, = sum of all items

N= number of items, = Arithmetic mean

Median: It is a middle value of the given data after arrangement in numerical order, either in ascending or descending order.

Mode: It is the number that is repeated more times in the given data.

Example: Derive the mean, median and mode for the given data

Sol:

To find median given data should be arranged in numerical order.

2. Ascending order ◊ Median = middle value =

3. Mode is the most repeated value. In the given problem is repeated 4 times. Mode

Calculation of Arithmetic mean for different types of series:

Individual Series: A set of all observations without grouping them under frequency.

Direct Method:

Shortcut Method:

where A is Assumed Mean, dx is deviation of x from Assumed mean.

Ex: 4, 3, 8, 9, 12, 10, 25, 10, 21 and 20 calculate Mean for the given individual series.

Direct Method: = = = 12.2

Shortcut Method: Assumed Mean A= 12,

= 12+=

Discrete Series: In discrete series data frequencies of a variable are given but the variable is without class interval. Formula for calculating arithmetic mean given below –

Direct Method: where f is frequency and N is the sum of frequencies.

Shortcut Method:

Example: Calculate arithmetic mean for the given data.

Number of children per family (x) | |||||||

Number of families (f) |

Solution:

x | f | fx | dx = x-A | fdx |

Direct Method:

.

Shortcut Method: Assumed mean A= 2

=