(Q6) A survey 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

Find the mode of this data.

Solution : Here the maximum class frequency is 8, and the class corresponding to this frequency is 3-5. So, the modal class is 3-5

Now,

  Modal class = 3-5, boundary limit (l) of modal class = 3, class size (h) = 2

  Frequency of the modal class (f1) = 8,

  Frequency of class preceding the modal class (f0) = 7,

  Frequency of class succeeding the modal class (f2) = 2.

Now, let us substitute these values in the formula-

Mode = l + [
f1 - f0
2f1 - f0 - f2
 ] × h
Mode = 3 + [
-
2 × - -
] × = 3 +
=

Therefore, the mode of the data above is