# Descriptive Statistics

## What type of indicators to use?

Nominal: Frequency, Mode

Ordinal: Frequency, Mode, Median

Scale, Ratio: Frequency, Mode, Median, Mean, Range, Std. Deviation, Skewness, Kurtosis, Range

## Measures of central tendencies

Mode: The most frequently occuring number.

Median: 156.000 Ft. It means: 50% of our respondents earn less then 156.000Ft and 50% of our respondents earn more then 156.000Ft.

Mean: the average. Example: The average monthly salary is 156.000 Ft. So, on average people earn 156.000 Ft per month. This is a good measure only when the variable is normally distributed since the mean value is influenced by outliers. If the data is not normally distributed then it is more appropriate to use the median then the mean.

## Measures of dispersions

Tells us more about how our data is distributed.

**Standard Deviation:** the average distance a score is from the mean. This tells us how widely spread out our distribution is. Low SD. means the values are close to the mean, whereas high SD means values are spread out over a large range.

So, the larger the deviation from 0 the greater consideration you might give towards transforming your data in some way to make it normal.

**Skewness** is a measure of symmetry of distributions. A perfectly normal distribution has a skewness statistics of 0.

Positive skewness: Mode < Median < Mean

Negative skewness: Mean < Median < Mode

**Kurtosis** will let us know if our data is peaked or flat.

The Kurtosis of a perfectly normal distribution is 3.

Example: Kurtosis=1.28 This indicates that there is a positive skewness, meaning our distribution is relatively peaked. We have relatively low outliers. It is a measure of the sheep of the curve. It measures if the bell of the curve is normal, flat or peaked.

**The variance:** is the squared standard deviation. It is not reported as frequently as the standard deviation.

**Range:** maximum – minimum.