Question

What is an arithmetic mean? How can it be computed in the case of ungrouped as well as grouped data? Illustrate with the help of hypothetical data

Answer 1

Step-by-step explanation:

Given that:

What is an arithmetic mean? How can it be computed in the case of un-grouped as well as grouped data? Illustrate with the help of hypothetical data.

To find: Definition of arithmetic mean.How to find mean for grouped and un-grouped data.

Solution:

Definition of Arithmetic mean:

Arithmetic mean is measure of central tendency.It is calculated by adding all the data together divided by total number of data or observation.

Formula to find arithmetic mean in case of un-grouped data:

Mean= Sum of all Observation/Total number of observation

Example for un-grouped data:

Let the marks of 10 students are given as follows

5,7,4,9,8,2, 4,7,9,6

N=10

Arithmetic mean= Sum of all observation/total observation

= (5+7+4+9+8+2+4+7+9+6)/10

=60/10

= 6

Arithmetic mean = 6 marks

Example for grouped data:

Find mean of the data given below

$\begin{tabular}{|c|c|c|}\cline{1-2}Class\:interval&frequency\\\cline{1-2}0-5&2\\\cline{1-2}5-10&5</p><p>\\\cline{1-2}10-15&8\\\cline{1-2}15-20&5\\\cline{1-2}Total&20\\\cline{1-2}\end{tabular}$

Solution:

$\begin{tabular}{|c|c|c|c|c|}\cline{1-4}Class\:interval &frequency(f_i)&class\:mark(x_i)&x_if_i\\\cline{1-4}0-5&2&2.5& 5\\\cline{1-4}5-10&5&7.5&37.5</p><p>\\\cline{1-4}10-15&8&12.5&100\\\cline{1-4}15-20&5& 17.5&87.5\\\cline{1-4} Total&20&&230\\\cline{1-4}\end{tabular}$

Class mark(xi)=( Lower limit of class+Upper limit of class)/2

$Mean=\frac{\Sigma x_i f_i}{f_i}$

Mean= 230/20=11.5

Hope it helps you.

Answer 2

Arithmetic Mean:

The arithmetic mean is the averaged value of the data whether it is grouped or ungrouped data. It is calculated by the sum of the data upon the number of data.

Un-Grouped Data:

Here:

The arithmetic mean is calculated by:

A.M. = Sum of observation/number of the observation

Let us consider the weight of 5 man:

55,70,84,96,85

AM= Sum of all observation/number of observation

AM =  (55+70+84+96+85)/5

AM = 390/5

AM = 78

AM = 78 Kg

Grouped Data:

Here:

The arithmetic mean is calculated by:

A.M = ∑xₙfₙ/fₙ

Let us consider the example:

Age of the student in class 4th

Xₙ                     Fₙ                       XₙFₙ

10                    12                         120

11                     6                           66

12                    2                           24

                  ∑Fₙ = 20                  ∑XₙFₙ = 210

A.M = ∑xₙfₙ/fₙ

AM = 210/20

AM = 10.5 years.