Question

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

Answer 1

Arithmetic mean is the most commonly used average or measure of the central tendency applicable only in case of quantitative data; it is also simply called the “mean”. Arithmetic mean is defined as:

“Arithmetic mean is a quotient of sum of the given values and number of the given values”.

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Answer 2

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?

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.