If mean of the following distribution is 211, then what is the value of (4p - 3q) ?

Class	100 - 150	150 - 200	200 - 250	250 - 300	300 - 350	Total
Frequency	4	p	12	q	2	25

 

Formula used:

Mean (x̅) = (Summation of fi xi) / (Summation of fi)

Where xi is the class mark and fi is the frequency.

Class Mark (xi) = (Lower Limit + Upper Limit) / 2

Calculation:

First, calculate the class mark (xi) for each class and then fixi:

From the total frequency, we have:

4 + p + 12 + q + 2 = 25

⇒ 18 + p + q = 25

⇒ p + q = 25 - 18

⇒ p + q = 7 ......(Equation 1)

Given Mean = 211

x̅  = (Summation of fixi) / (Summation of fi)

⇒ 211 = (3850 + 175p + 275q) / 25

⇒ 211 × 25 = 3850 + 175p + 275q

⇒ 5275 = 3850 + 175p + 275q

⇒ 5275 - 3850 = 175p + 275q

⇒ 1425 = 175p + 275q

⇒ 1425/25 = 175p/25 + 275q/25

⇒ 57 = 7p + 11q ......(Equation 2)

From Equation 1, p = 7 - q.

Substitute p in Equation 2:

57 = 7(7 - q) + 11q

⇒ 57 = 49 - 7q + 11q

⇒ 57 - 49 = 4q

⇒ 8 = 4q

⇒ q = 8/4

⇒ q = 2

Substitute q = 2 in Equation 1:

p + 2 = 7

⇒ p = 7 - 2

⇒ p = 5

Now, find the value of (4p - 3q):

4p - 3q = 4 × 5 - 3 × 2

⇒ 4p - 3q = 20 - 6

⇒ 4p - 3q = 14