Question 1 [6 marks] For 2 marks each, prove the following properties of the sample mean (a) Zim1(xi+0) = x + c (where c is a constant) (b) Zin CX = CX n (c) Zi=1(xi - x) = 0 Question 2 [10 marks] Voice detection is one of the important stages in individual's recognition and identification. A model was tested from 30 different speakers saying the same vowel. The researcher wanted to find out if what kind of features that could be extracted from voice biometrics. The magnitude responses (dB) were as follows: 17 27 14 18 6 26 23 18 9 17 22 29 28 17 10 24 15 13 25 13 22 21 23 15 14 25 18 21 5 (a) State which measure of central location would be more appropriate, if necessary. the responses by citizens on a five-point rating scale to the statement: "South Africa should be divided into two time zones." [2] (b) Calculate the coefficient of variation [5] (c) How many voice biometric responses that are below the upper quartile? Show all calculations [3]