Question

A random sample from a given population gives the following numerical values: x1, y2, · · · , xn:

(a) What is meant by the expression “random sample”?

(b) Prove that ∑n j=1 (xi − x¯) = 0.

(c) Indicate the type of measures and state one advantage and disadvantage of the in the following table:

Measure Type Advantage Disadvantage

Mean

Median

Mode

Range

Answer 1

(a) The term "random sample" means that each and every sample observations are drawn with equal probability from the Population.

(c) Mean, Median, Mode these three are measures of location , used to get idea regarding measure of central tendency. Whereas Range is a measure of dispersion, used to figure out the degree of scatter ness

Advantage & disadvantage:

1. Mean is easy to compute and easy to comprehend, but it is heavily affected by outlier observations

2. Median is a robust measure and least affected by outliers but it is not based on all observations like mean.

3. Mode is also robust measure similar to median, but it suffers from the problem of non-uniqueness.

4. Range is the most easily computable measure based only on largest and smallest observations, but since it is not based on the whole data, does not give a compact scenerio of scatterness.

(b) done in photo