Question

Given the following sample of 20 numbers: 12 41 48 58 14 43 50 59 15 45 52 72 18 45 54 78 41 47 56 79 (a) Compute mean, variance and standard deviation. (b) If the largest value in the above set of numbers is changed to 500, to what extent are the mean and variance affected by the change? Justify your answer.

Answer 1

Answer:

Explanation:

(a) mean=46.35, standard deviation=19.114, variance=365.345

(b) mean=67.4, standard deviation=100.793, variance=10159.223

Answer 2

Answer:

The answer is mean 46.35, variance 365.32, standard deviation 19.11.

Explanation:

a)

Mean = μ = ∑x/N =  46.35

Variance = σ$^{2}$ =  ∑(x-μ)$^{2}$/N = 365.32

Standard deviation = σ =  $\sqrt{var}$ = 19.11

b) If the number 79 is changed to 500, then

Mean = μ = ∑x/N =  67.4

Variance = σ$^{2}$ =  ∑(x-μ)$^{2}$/N = 10158.84

Standard deviation = σ =  $\sqrt{var}$ = 100.79

c) The mean is not affected as much as the variance by the change. This might be due to the fact that mean does not depend on a single value as compared to variance which is affected by all sample numbers.

#SPJ3