WAEC Further Mathematics 2016 Theory question 106

Theory question 106

Statistics

The mean of the numbers 1, 4, k, (k + 4) and 11 is (k + 1). Calculate the: (a) Value of k; (b) standard deviation.

Show the model answer

Model answer

(a) (20 + 2k)/5 = k + 1, so 20 + 2k = 5k + 5 and k = 5.
(b) Numbers 1, 4, 5, 9, 11; mean 6. Squared deviations 25, 4, 1, 9, 25 add to 64.
SD = √(64/5) = √12.8 ≈ 3.58.

Explanation

Find k, then list the actual numbers.