Question

Monthly consumption of electricity (in units) of families in a certain locality is given below:

205, 201, 190, 188, 194, 172, 210, 225, 215, 232, 260, 230.

Calculate electricity consumption (in units) below which 25% of families lie.

Answer 1

Arrange the data in ascending order

Given values (units):

205, 201, 190, 188, 194, 172, 210, 225, 215, 232, 260, 230

Arranged:

172, 188, 190, 194, 201, 205, 210, 215, 225, 230, 232, 260

Q1 position `= (n+1)/4`

Q1 position `= (12+1)/4 = 13/4` = 3.25

So Q1 lies between the 3rd and 4th values.

3rd value = 190

4th value = 194

Q1 = 190 + 0.25 × (194 − 190)

Q1 = 190 + 0.25 × 4 = 190 + 1

= 191