Question

In the formula for the variance Σ (x- μ)^2/n, what is the sum if we don't square the (x - H) values? [Hint: There is a special name for this sum.] In testing a new drug, researchers found that 20% of all patients using it will have a mild side effect. A random sample of 25 patients using the drug is selected. Find the mean and standard deviation of patients having a mild side effect.

Answer 1

(1)

Formula for the variance is given by:

$\sigma ^{2}=\frac{\sum (x-\mu )^{2}}{n}$

If we don't square the (x- $\mu$ ):

Sum of the deviations from mean is zero.

i.e.,

$\frac{\sum (x-\mu )}{n}=0$

So,

Answer is:

0

(b)

Binomial Distribution

n = 25

p = 0.20

q = 1 - p = 0.80

(i) Mean = np = 25 X 0.20 = 5

(ii) Standard Deviation = $\sqrt{npq}=\sqrt{25\times 0.20\times 0.80}=2$