Question

If the mean of the following distribution is 6, find the value of p.

xi	2	4	6	10	p + 5
fi	3	2	3	1	2

Answer 1

Step 1: Organize the data

Based on the table provided, let’s calculate the products of the values (x_i) and their frequencies (f_i):

xi	fi	fi × xi
2	3	2 × 3 = 6
4	2	4 × 2 = 8
6	3	6 × 3 = 18
10	1	10 × 1 = 10
p + 5	2	2(p + 5) = 2p + 10
Total	Σfi = 11	Σ(fi × xi) = 52 + 2p

Step 2: Set up the equation

We are given that the mean `(barx)` is 6. Plugging the totals from our table into the mean formula:

`6 = (52 + 2p)/11`

Step 3: Solve for p

1. Multiply both sides by 11 to clear the fraction:

66 = 52 + 2p

2. Subtract 52 from both sides:

66 – 52 = 2p

14 = 2p

3. Divide by 2:

p = 7

The value of p is 7.