Question

If the mean of the frequency distribution is 8.1 and Σf_ix_i = 132 + 5k, Σf_i = 20 then find k.

Answer 1

1. State the mean formula

The mean `(barx)` of a grouped frequency distribution is calculated using the formula:

` barx = (Σf_ix_i)/(Σf_i)`

2. Substitute given values

Substitute the given values into the formula:

`barx = 8.1`

Σf_ix_i = 132 + 5k

Σf_i = 20

`8.1 = (132 + 5k)/20`

3. Solve for k

Multiply both sides by 20 to clear the denominator:

8.1 × 20 = 132 + 5k

162 = 132 + 5k

Subtract 132 from both sides:

162 – 132 = 5k

30 = 5k

Divide by 5:

`k = 30/5`

k = 6