# Quantitative data collection and analysis

## Averages and Percentiles

There are 3 main measures of central tendency:

• The mean
• The mode
• The median

These values show the tendency of observations to group around a particular value or group.

Outliers are untypical extreme high or low values.

The mean is commonly called the average.

Mean value = Total of (sometimes referred as Sum of) all the values ÷ Number of observations

The Mean can be effected by any outliers (extreme values at either end of the distribution).

It is typically denoted by  (sample mean)

The mean of the population is denoted by ${\displaystyle \mu }$ or ${\displaystyle \mu _{x}}$ (mu).

The mode is the value that occurs most often.

This can be useful for categories when you have no mean or median.

The median is the middle (or central) value.

Percentiles divide a set of data into hundredths (100 equal parts)

It is useful to find a value at or below which a specified percentage of the scores in a distribution fall.

e.g. the 75 percentile  is where 75% of observations in a distribution will lie at or below.

e.g. if the 40% percentile for a exam was 45 this would mean that 40% of people  who took the exam got a mark of 45 or lower.

The Lower Quartile (LQ) is the 25th percentile

The Median is the 50th percentile

The Upper Quartile (UQ) is the 75th percentile