# 2. Measurement Scales

## a. distinguish between descriptive statistics and inferential statistics, between a population and a sample, and among the types of measurement scales;

## b. define a parameter, a sample statistic, and a frequency distribution;

What is a Nominal measurement scale?

- Consists of assigning items to groups or categories

- Qualitative

What are some examples of Nominal measurements?

Religious preference, sex, race. Things that are not numerical and don't need to be ordered.

What is an Ordinal measurement scale?

Ordinal measurements are categorical measures with higher numbers meaning higher values. Starting point does not need to be 1, can be any set of numbers.

What is an Interval measurement scale?

Quantitative measurements with equal intervals between each value.

What is the ratio measurement scale?

Quantitative measures with a true zero point and relative score. A measure of 10 is twice as big/good as 5. Examples are rate of return and money, Kelvin temperature.

What does the acronym NOIR stand for and why is it important?

- NOIR = Nominal, Ordinal, Interval, Ratio

- It's important to know that the measurement scales get stronger as you go from start (N) to finish (R).

Which letter of NOIR would be used for the number of goals scored by a soccer player in a season?

Ratio. Goals scored can't go below zero, and 10 goals is twice as good as 5 goals.

Which letter of NOIR would be used for the temperature in Farenheit?

Interval. Temperatures are always measured on interval scale because they are equal distance apart and can be added/subtracted, but one temperature is not necessarily better/worse than another.

Which letter of NOIR would be used for the relative positions of contestants in a beauty pageant?

Ordinal. A position is an indicator of rank.

Which letter of NOIR would be used for the speed at which a vehicle travels?

Ratio. Speed is zero based and a bigger number is faster than a smaller number.

Which letter of NOIR would be used for the the allocation of the number "1" to boys and "2" to girls in a class?

Nominal. This is categorical labels

Which letter of NOIR would be used to rate stock performance rating as (5) Superior, (4) above average, (3) average, (2) below average, (1) poor?

Ordinal. The data is quantitative but the difference between the ranks cannot be determined in a meaningful way.

##### Source:

- CFA