Question

A survey was conducted by a group of students as a part of their environmental awareness program, in which they collected the following data regarding the number of plants in 200 houses in a locality. Find the mean number of plants per house.
Number of plants: 0-2 2-4 4-6 6-B 8-10 10-12 12-14
Number of houses: 1 2 1 5 6 2 3
Which method did you use for finding the mean, and why?

Answer 1

DIRECT METHOD:

In this method find the class marks of class interval. These class marks would serve as the representative of whole class and are represented by xi. For each class interval we have the frequency fi corresponding to the class mark xi.

Class marks = ( lower limit + upper limit)/2

Then find the product of fi, & xi for each class interval. Find Σ fi & Σ fixi.

Use the formula :  

MEAN = Σfixi/ Σfi

[‘Σ’ Sigma means ‘summation’ ]

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfixi = 162 ,Σfi = 20

MEAN = Σfixi/ Σfi

Mean = 162/20

Mean = 81/10 = 8.1

Hence, the mean number of plants per house is 8.1 .

Here, we use DIRECT METHOD for finding the mean because this is the easiest method from the other methods(STEP DEVIATION METHOD, ASSUMED MEAN METHOD).

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer :

The mean number of plants per house is 8.1 .

Step-by-step explanation :

Direct Method -

We will be finding the mean by using direct method since it would be easy as compared to others.

In direct method, we find the class marks of class interval. The class marks would be represented by $x_i$. Class marks can be calculated using the following formula i.e.,

$Class\:marks=\frac{(lower\:limit+upper\:limit)}{2}$

To find the mean, use the formula,

$Mean=\frac{\Sigma f_{i}x_{i}}{\Sigma f_i}$

where $\Sigma$ means summation.

Frequency Distribution Table -

$\begin{tabular}{|c|c|c|c|}\cline{1-4}No.\:of\:plants & x_i & f_i & f_{i}x_{i}\\ \cline{1-4}0-2 & 1 & 1 & 1\\ \cline{1-4}2-4 & 3 & 2 & 6\\ \cline{1-4}4-6 & 5 & 1 & 5\\ \cline{1-4}6-8 & 7 & 5 & 35\\ \cline{1-4}8-10 & 9 & 6 & 54\\ \cline{1-4}10-12 & 11 & 2 & 22\\ \cline{1-4}12-14 & 13 & 3 & 39\\ \cline{1-4} & & \Sigma f_{i}=20 & \Sigma f_{i}x_{i}=162\\ \cline{1-4}\end{tabular}$

Since, mean -

$\implies \frac{\Sigma f_{i}x_{i}}{\Sigma f_i}$

$\implies \frac{162}{20}$

$\implies \frac{81}{10}$

$\implies 8.1$