Question

16. If the mean of the following distribution is 2.6, then y
xi
1
2
3
4
5
Fi
4
5
Y
1
2
OR
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
numbers of plants per houses.
Number of plants
0-2
2-4
4-6
6-8
8-10
10-12
12-14
Number of houses
1
2
1
5
6
2
3​

Answer 1

Answer:

SEE BELLOW

Step-by-step explanation:

1. X=1,2,3,4,5

F=4,5,k,1,2

Mean =2.6

Mean =€fx/€f

2.6=(1x4+2x5+3xk+4x1+5x2)/4+5+k+1+2

2.6=(4+10+4+10+3k)/12+k

2.6=(28+3k)/12+k

2.6(12+k)=(28+3k)

31.2+2.6k=28+3k

31.2-28=3k-2.6k

3.2=0.4k

K=3.2/0.4

K=8

2. Using direct method to calculate mean :

No. of plants No. of houses x

i

f

i

.x

i

0-2 1 1 1

2-4 2 3 6

4-6 1 5 5

6-8 5 7 35

8-10 6 9 54

10-12 2 11 22

12-14 3 13 39

Σf

i

=20 Σf

i

.x

i

=162

Mean=

Σf

i

Σf

i

.x

i

=

20

162

=8.1plants

We used direct method for finding the mean as the width of the class is very small and also the frequency for each class have very small values. Thus, it will be easy to calculate.

Hope this will help you.

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