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 x₁, x₂, . . ., xₙ are observations with frequencies f₁, f₂, . . ., fₙ respectively. This means observation x₁ occurs f₁ times, x₂ occurs f₂ times, and so on
x is the class mark for each interval.
We can find the value of x by using class mark, x₁ = (Upper limit + Lower limit)/2
Now, the sum of the values of all the observations = f₁x₁ + f₂x₂ + . . . + fₙxₙ, and the number of observations = f₁ + f₂ + . . . + fₙ.
So, the mean of the data is given by
x = (f₁x₁ + f₂x₂ + ....... + fₙxₙ) / (f₁ + f₂ + ...... + fₙ)
x = Σfᵢxᵢ / Σfᵢ where i varies from 1 to n.
From the table it can be observed that,
Σfᵢ= 20
Σfᵢxᵢ = 162
Mean, x = Σfᵢxᵢ / Σfᵢ
= 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 xᵢ and fᵢ are small.
☛ Check: NCERT Solutions Class 10 Maths Chapter 14
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
Summary:
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. 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.
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