An experiment conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:
| Family size | 1-3 | 3-5 | 5-7 | 7-9 | 9-11 |
|---|---|---|---|---|---|
| Number of families | 7 | 8 | 2 | 2 | 1 |
The mode of the given data is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3.286
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, \(h\) the class width, \(f_1\) its frequency, and \(f_0\), \(f_2\) the frequencies of the classes before and after it.
Modal class: 3-5 (frequency 8, the highest)
\(l=3\), \(h=2\), \(f_1=8\), \(f_0=7\), \(f_2=2\)
\(\displaystyle \text{Mode}=3+\frac{8-7}{16-7-2}\times2=3+\frac{2}{7}\approx3.286\)