Question

Seven of the eight numbers in a distribution are 11, 16, 6, 10, 13, 11, 13 Given that the median of the distribution is 12, find the mean of the distribution.

(a) 12

(b) 11

(c) 11.6

(d) 12.2

Answer 1

Correct option is (c) 11.6

Let the 8th number be x

Therefore, when we write in ascending order we get

6, 10, 11, 11, x, 13, 13, 16.

Now median is 12 (given)

Therefore , \(\frac{11 + x}2\) = 12

⇒ 11 + x = 24

⇒ x = 24 - 11

⇒ x = 13

So eight number x will be 13.

Now we have 6,10,11,11,13,13,13,16.

So to find mean

x = \(\frac{6 + 10 + 11 + 11 +13+ 13 + 13 +16}{8}\)

x = \(\frac{93}8\)

x = 11.6

Answer 2

Note: Have to be careful here.  This question is ambiguous since it does not say where the "missing" number falls in the distribution and we do not know what that number is.  For example, say the eighth number was 16.

Then we would have in ascending order: 6, 10, 11, 11, 13, 13, 16, 16

The median here is 12 satisfying the constraints of the problem but now the mean is 12.