Question

The mean of 5, 7, 8, 4 and m is n and the mean of 5, 7, 8, 4, m and n is m. Find the values of m and n.

Answer 1

Given:

Let the mean of 5, 7, 8, 4 and m be n and the mean of 5, 7, 8, 4, m and n be m.

By definition, Mean = `"Sum of terms"/"Number of terms"`

Step-wise calculation:

1. Mean of 5, 7, 8, 4 and m is n:

`(5 + 7 + 8 + 4 + m)/5 = n`

24 + m = 5n   ...(Equation 1)

2. Mean of 5, 7, 8, 4, m and n is m:

`(5 + 7 + 8 + 4 + m + n)/6 = m`

24 + m + n = 6m

⇒ 24 + n = 5m   ...(Equation 2)

3. Solve the system:

From (1): m = 5n – 24.

Substitute into (2): 24 + n = 5(5n – 24)

= 25n – 120

24 + n = 25n – 120

144 = 24n

⇒ n = 6

Then m = 5n – 24

= 30 – 24

= 6