Types of data, frequency distribution and histograms

Statistics

Science incorporating the knowledge and skills to organise, summarise, and analyse data

Nominal data

Mutually exclusive

No other mathematical operations permitted

Exhaustive - every observation must belong to a category

Ordinal data

Based on relative ranking/ratings

But unknown distances between e.g. ranks of Unis - don't know HOW much better one is than the othe

 

Interval data

Distance between values IS meaningful - and known

Known units of measurement

 

Ratio data

Zero = Absence of characteristic

Includes most quantitative data

E.g. weight, age etc.

Frequency distribution

Grouping of quantitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class

Class frequency

Number of observations in each class

How to construct a frequency distribution table

1. Decide the number of classes using this rule: choose the smallest number for k such that 2^k > n, where n = total number of observations

2. Determine class intervals: Find the range (min - max value) in the whole data set, then divide by the number of classes - round down/up if necessary to get a whole number

3. Set individual class limits: e.g. if the lowest value in the data set is 10.3 start the first class at 10.0, and say the class interval = 5, the first class would be 10 - 14.9, the second class would be 15 - 19.9 etc.

4. Determine the frequency for each class interval e.g. how many data values fall between 10 - 14.9 for the first class

5. Add relative frequency: frequency divided by n (total number of data values in the set)

6. Add cumulative frequency - just add frequency from previous class to the next class etc.

Histogram

A graph in which the classes are marked on the horizontal axis and the class frequencies on the vertical axis - Class frequencies represented by the height of the bars AND bars drawn ADJACENT to each other to show continuous nature of the data

Frequency polygon

Attaches line segments to the midpoints of each class interval