Objectives of Classification

To condense the data for easy understanding

To help comparison

To eliminate unnecessary details

To make decision making possible

To enable further statistical treatments

To identify main features of the data

** i. Chronological Classification**

It is the arrangement of data in ascending or descending order with reference to time.

Chronological Classification | |
---|---|

Year | Population |

2009 | 567 |

2010 | 638 |

2011 | 736 |

2012 | 758 |

** ii. Geographical Classification**

It is the arrangement of data with reference to geographical location such as countries, states (Spatial).

Geographical Classification | |
---|---|

States | Production of Rice |

Andhrapradesh | 1200 |

Tamilnadu | 950 |

Kerala | 830 |

** iii. Qualitative Classification**

It is the arrangement of Data on the basis of some qualities or Values or attributes such as colour, sex, religion, literacy.

Qualitative Classification | |
---|---|

States | Literacy |

Kerala | 99.5% |

Karnataka | 95.6% |

Bihar | 68% |

** iv. Quantitative Classification**

It is the classification of Data on the basis of some quantitative measurement such as weight, price, cost.

Quantitative Classification | |
---|---|

Companies | Sales |

Hundai | 800 |

Tata | 638 |

Maruti | 736 |

**Quantitative Data:**

Data can be measured numerically-eg; Income, Production, Price, Cost..

**Qualitative:**

Data cannot be measured numerically- eg; Health, Intelligence, Ability..Also termed as Attributes.

Variable

A variable is that characteristic whose value is capable of changing from unit to unit. Depending on the way they vary, they are broadly classified Into two types:

**CONTINUOUS****DISCRETE**

**Indivisual Series (Simple Array)**

Each value of the variable occurs usually once. It can be arranged either in ascending or descending order.

Individual Series | |
---|---|

Number of workers | Wage (Rs) |

1 | 500 |

2 | 600 |

3 | 550 |

**Discrete Series (Frequency Array)**

Certain items occurs many time in the data. It can be arranged either in ascending or descending order.

Discrete Series | |
---|---|

Number of Children per couple | Number of Couples (Frequency) |

0 | 21 |

1 | 19 |

2 | 10 |

Total | 50 |

**Continuous Series**

Different values of the variable are stated in a continuous manner with respect to their frequencies.

Continuous Series | |
---|---|

Marks (Class) | Number of Students (Frequency) |

0 - 10 | 5 |

10 - 20 | 10 |

20 - 30 | 17 |

30 - 40 | 13 |

40 - 50 | 5 |

Total | 50 |

Frequency Distribution

An orderly arrangement of data classified according to the magnitude of observations in different classes along with their corresponding class frequencies is known as frequency distribution. Frequency means the number of times a value or item occurs.

Construction of Frequency Distribution

**Selection of Class**

- There is no hard and fast rule to determine number of classes
- A class should not be too big or too small
- There should not be too much classes or too short

**Class Limit**

- The class limits are the lowest and the highest values that can be included in the class.
- It is the two ends of a class.
- In class 20 – 30, 20 is called the lower class limit and 30 is called upper class limit.

**Class Interval**

- It is the difference between the upper and lower class limits.
- Class interval is also known as class width or class size.
- The class interval of the class 50 – 100 is 50 (100 – 50 = 50)

**Class Midpoint**

- It is the middle value of a class. It is also known as mid value or class mark.
- It lies half way between the lower and upper class limits of a class.

**Magnitude of Class Interval**

- The difference between lower and upper class boundaries is called the magnitude of a class interval

**Class frequency**

- The number of observation corresponding to a particular class is known as the class frequency.

How to find Frequency of distribution ?

We had seen that frequency means the number of times a value or item occurs and we have to count the number of times each value of the variable is repeated in the data to get the frequency. If the data is large, the counting simply will invite errors. For this we use the method of tally marks. Tally marks are vertical bars (/) used for counting.

Using tally marks, we can create a frequency distribution. For that first we will draw a table with three columns. In the first column we write the class, in the second we write tally marks, and in the third frequency. All the entries in the first column are filled with classes. Now look at the data given. The first entry is 70. That-will fall in the class 70 - 80. Now strike off the entry 70 in the data and and put a tally mark in the second column right to the class 70 - 80. The second entry is 54. That will fall in the class 50 - 60. Now strike off the entry 54 in the data and put a tally mark in the second column right to the class 50 - 60. This process will be repeated up to when all the entries in the data gone stroked off. One more thing to notice is that, after placing 4 tally marks vertically, for the fifth we put the tally mark horizontally to cut the first four tally marks, so that this gives us a block of 5. For the sixth we put another tally mark vertically leaving some space from the first block. Look at the given below table, it is completed by doing the above said process.

Frequency Distribution with Tally Mark | ||
---|---|---|

Class | Tally Marks | Marks |

0 - 10 | //// / | 6 |

10 - 20 | /// | 3 |

20 - 30 | //// //// //// //// //// | 25 |

30 - 40 | //// //// //// / | 16 |

40 - 50 | //// //// //// //// | 19 |

50 - 60 | //// //// /// | 13 |

60 - 70 | //// | 5 |

70 - 80 | //// /// | 8 |

80 - 90 | //// | 4 |

90 - 100 | / | 1 |

Total | 100 |

**Exclusive Method**

Exclusive Classes | |
---|---|

Marks (Class) | |

0 - 10 | |

10 - 20 | |

20 - 30 | |

Inclusive Method

Under this method the classes, are so fixed that the upper limit of one class is included in the class itself.

Inclusive Classes | |
---|---|

Marks (Class) | |

0 - 9 | |

10 - 19 | |

20 - 29 | |

How to Convert Inclusive Classes into Exclusive Classes ?

Find the difference between the upper limit of a class and the lower limit of the next class. Find half the difference. Subtract this number from all the lower limits and add this number to all the upper limits.

Inclusive Classes | |
---|---|

Marks (Class) | |

0 - 9 | |

10 - 19 | |

20 - 29 | |

Difference between the upper limit of a class and the lower limit of the next class = 10 – 9 = 1

Half the difference : \( {{\frac{ 1}{2}} } \) or (0.5).

Now we can get exclusive type class as given below.

Exclusive Classes | |
---|---|

Marks (Class) | |

-0.5 - 9.5 | |

9.5 - 19.5 | |

19.5 - 29.5 | |

Cumulative Series

In a cumulative series the frequencies are progressively totalled and aggregates are shown.

Cumulative Series | |
---|---|

Marks (Class) | Number of Students (Frequency) |

Marks below 10 | 12 |

" below 20 | 18 |

" below 30 | 24 |

" below 40 | 30 |

" below 50 | 36 |

The cumulation may be upward or downward.

Open end Class

If the lower limit of the first class or upper limit of the last class are not given, such series are called open end class series.

Open end Class | |
---|---|

Marks (Class) | Number of Students (Frequency) |

Marks below 10 | 4 |

10 - 20 | 6 |

20 - 30 | 6 |

30 - 40 | 9 |

40 and above | 5 |

Unequal Class

If all classes in the distributions are not equal, it can be called unequal class distribution.

Unequal Class | |
---|---|

Marks (Class) | Number of Students (Frequency) |

0 - 10 | 4 |

10 - 20 | 6 |

20 - 25 | 6 |

25 - 30 | 9 |

30 - 40 | 5 |

**Univariate Distribution.**

Frequency distribution with single variable is called Univariate.

Univariate Distribution | |
---|---|

Marks. | Number of Students. |

40 - 50 | 5 |

50 - 60 | 8 |

60 - 70 | 15 |

70 - 80 | 20 |

80 - 90 | 7 |

90 - 100 | 2 |

**Bivariate Distribution.**

Frequency distribution with two variables is called Bivariate.

Bivariate distribution | ||||
---|---|---|---|---|

Sales. | 100 - 200 | 200 - 300 | 300 - 400 | 400 - 500 |

Cost. | ||||

40 - 50 | 5 | 3 | 2 | 1 |

50 - 60 | 8 | 4 | 3 | 1 |

60 - 70 | 8 | 3 | 1 | 1 |

70 - 80 | 6 | 1 | 2 | 1 |

80 - 90 | 4 | 1 | 1 | 2 |