# Identification under individual and discrete series by inspection method

20/10/2022**Individual Series:**

The terms are arranged in any order. Ascending or Descending. If each term of the series is occurring once, then there is no mode, otherwise the value that occurs Maximum Times is known as Mode. Mode is often denoted by Z.

**Method to Calculate Mode:**

(1) Arrange the terms in ascending or descending order (Preferably Ascending)

(2) Note the term occurring maximum times if it is or is a unique one.

(3) This term is Mode. (Z).

(Note:-If all terms occur once or some terms occur equal number of times, we can’t find Z by this method)

Example 1. Find Mode for following data |
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12 | 14 | 16 | 18 | 26 | 16 | 20 | 16 | 11 | 12 | 16 | 15 | 20 | 24 |

Solution: Arrange above data in ascending order |
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11 | 12 | 12 | 14 | 15 | 16 | 16 | 16 | 16 | 18 | 20 | 20 | 24 | 26 |

**Here we get 16 four times, 12 and 20 two times each and other terms once only. Thus Z = 16**

** Discrete Series:**

**Here the mode is known by Inspection Method only. Here that variable is the Mode where the frequency is highest. But this method is applicable only if ;**

(1) There is a gradual rise or fall in the sequence of frequencies.

(2) The highest frequency and the next highest frequency are not too close

(3) Maximum frequency is not repeated.

Example 1. Find Mode for following data |
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X: |
4 |
7 |
11 |
16 |
25 |

f: |
3 |
9 |
14 |
21 |
13 |

**Solution:**

In the above given series highest frequency is 21 and variable corresponding to i this frequency is 16. Thus Mode (Z) is 16.

Special Note:-But, however sometimes it becomes impossible to locate Mode by inspection as concentration of frequencies is not in a unique manner or fashion as desired for this method.

For such a distribution we have to prepare (1) grouping Table and (2) Analysis

**Table:**

**(1) Grouping Table: It has Six Steps as given below.**

(1) Frequencies are taken.

(2) Frequencies are added in two(s).

(3) Leaving first item, frequencies are added in two(s)

(4) Frequencies are added in threes.

(5) Leaving first frequency, frequencies are added in three (s)

(6) Leaving first two frequencies, frequencies are added in three (s).

In each case, take maximum total and put it in a circle or a box to distinguish it from others.