Descriptive Stats - Chapter 2 (Session 4) - Theory

Question 1

What are the 3 characteristics which are used to describe the data profile of random variable?

Answer 1

Measure of location: Central + non-central, Central location is a
representative ‘middle’ value of concentration of the data.

Measures of spread (or dispersion): extent to which the data values are spread about the central
location value.

Measure of shape (skewness): identifies the shape (or degree of symmetry) of the data values about the central
location measure.

Question 2

What are the 3 commonly used central location statics?

Answer 2

(a) the arithmetic mean (also called the average)
(b)the median (also called the second quartile, the middle quartile or the 50th percentile)
(c) the mode (or modal value).

Question 3

What are the non-central location measures?

Answer 3

Quartiles are non-central measures that divide an ordered data set into quarters (i.e. four
equal parts).
The lower quartile, Q1, is that data value that separates the lower (bottom) 25% of
(ordered) data values from the top 75% of ordered data values.
The middle quartile, Q2, is the median. It divides an ordered data set into two equal halves.
The upper quartile, Q3, is that data value that separates the top (upper) 25% of (ordered)
data values from the bottom 75% of ordered data values.