A survey conducted on 20 house holds in a locality resulted in the following frequency table.
|
Family size |
1-3 |
3-5 |
5-7 |
7-9 |
9-11 |
|
No. of families |
7 |
8 |
2 |
2 |
1 |
What is the mode of this data?
Answer & explanation
Correct answer: option 1
We know that,
Mode = l+ (f1- f0)/(2f1 - f0 - f2) × h
Here
l = Lower limit of the modal class
f1 = Frequency of the modal class
f0 = Frequency of the previous modal class
f2 = Frequency of the after-modal class
h = size of the modal class
Here Range 3-5 has the highest frequency.
So, modal class = 3-5
l= 3, f0 = 7, f1 = 8, f2 = 2, h = 2
Mode = 3 + (8 - 7)/(2× 8 - 7 - 2) × 2
= 3 + 1/7 × 2
= 3 + 2/7
= 3 + 0.286 = 3.286 or $3\frac{2}{7}$