A survey conducted on 20 households 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
The correct answer is Option (1) → \(3\frac{2}{7}\)
For grouped data the mode lies in the modal class, the class with the highest frequency, and is found by the formula
\(\displaystyle \text{Mode}=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h\)
where \(l\) is the lower limit of the modal class, \(f_1\) its frequency, \(f_0\) and \(f_2\) the frequencies of the classes before and after it, and \(h\) the class width.
Highest frequency 8, so the modal class is 3-5: \(l=3\), \(f_1=8\)
Class before it (1-3): \(f_0=7\); class after it (5-7): \(f_2=2\); width \(h=2\)
\(\displaystyle \text{Mode}=3+\frac{8-7}{16-7-2}\times2=3+\frac{2}{7}=3\frac{2}{7}\)