The mean of the numbers 1, 4, k, (k + 4) and 11 is (k + 1). Calculate the :
(a) value of k ;
(b) standard deviation.
Explanation
(a) (frac{1 + 4 + k + (k + 4) + 11}{5} = k + 1)
(frac{2k + 20}{5} = k + 1)
(2k + 20 = 5(k + 1) implies 2k + 20 = 5k + 5)
(20 – 5 = 5k – 2k implies 15 = 3k)
(k = 5)
(b) Mean (bar{x} = 6)
|
Mark (x) |
freq (f) | fx | (x^{2}) | (fx^{2}) |
| 1 | 1 | 1 | 1 | 1 |
| 4 | 1 | 4 | 16 | 16 |
| 5 | 1 | 5 | 25 | 25 |
| 9 | 1 | 9 | 81 | 81 |
| 11 | 1 | 11 | 121 | 121 |
| 5 | 30 | 244 |
(sigma = sqrt{frac{sum fx^{2}}{sum f} – (frac{sum fx}{sum f})^{2}})
= (sqrt{frac{244}{5} – (frac{30}{5})^{2}})
= (sqrt{48.8 – 36})
= (sqrt{12.8} = 3.58)