Question

Question 5 a. (1 mark) Define a simple random sample of size n · (1 mark The following statement is True or False. Empirical Rule is applicable any data set (1 mark) A data set contains a data point that is extremely small, when compared to the rest of the data. The sample mean is (greater than)/ (less than) / (equal to) the c. sample median. d. (2 marks) For the following data set, 10, 16, 18, 22, 27 the sample mean is and the sample standard deviation is

Answer 1

a) Simple random sampling is a sampling technique where every item in the population has an even chance and likelihood of being selected in the sample of size n.

b) FALSE

Empirical Rule is an approximation that applies only to data sets with a bell-shaped relative frequency histogram.

c) The sample mean is less than the sample median.

d) Sample mean, $\dpi{100} \bar x$ =

$\dpi{100} \bar x=\frac{10+16+18+22+27}{5}= \textbf{18.6}$

Sample standard deviation, s =

$\dpi{100} s = \sqrt{\frac{\Sigma(x-\bar x)^2}{n-1}}$

$\dpi{100} =\sqrt{\frac{(10-18.6)^2+(16-18.6)^2+(18-18.6)^2+(22-18.6)^2+(27-18.6)^2}{5-1}}$

$\dpi{100} =\sqrt{40.8} = \textbf{6.3875}$