# A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house

Which method did you use for finding the mean, and why?

**Solution:**

We solve this problem by any method of finding mean but here we will use the direct method to solve this question because the data given is small.

As we know, the mean of observations is the sum of the values of all the observations divided by the total number of observations.

We know that x_{1}, x_{2}, . . ., x_{n} are observations with frequencies f_{1}, f_{2}, . . ., f_{n }respectively. This means observation x_{1} occurs f_{1} times, x_{2} occurs f_{2} times, and so on

x is the class mark for each interval, you can find the value of x by using class mark, x_{1} = (upper limit + lower limit)/2

Now, the sum of the values of all the observations = f_{1}x_{1} + f_{2}x_{2} + . . . + f_{n}x_{n}, and the number of observations = f_{1} + f_{2} + . . . + f_{n}.

So, the mean of the data is given by

x = (f_{1}x_{1} + f_{2}x_{2} + ....... + f_{n}x_{n}) / (f_{1} + f_{2} + ...... + f_{n})

x = Σf_{i}x_{i-}/ Σf where i varies from 1 to n.

From the table it can be observed that,

Σf_{i}= 20

Σf_{i}x_{i} = 162

Mean, x = Σf_{i}x_{i }/ Σf_{i}

= 162/20

= 8.1

Thus, the mean number of plants in each house has 8.1.

Here, we have used the direct method because the value of x_{i} and f_{i} are small.

**Video Solution:**

## A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house. Which method did you use for finding the mean, and why?

### NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.1 Question 1 - Chapter 14 Exercise 14.1 Question 1:

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house. Which method did you use for finding the mean, and why?

The mean number of plants in each house is 8.1 and the method used was the direct method because the value of xi and fi are small