#### Statistics to Describe a Data Set

Continuous Data

Values that are measured (example is measuring arm length)

Discrete Data

Data that is obtained by counting not measuring.

Numerical Data

Known as quantitative data. Represents variables that can be measured and recorded (either interval or ratio).
This would be continuous data.

Categorical Data

Known as qualitative data. Represents variables that can be observed and recorded as a category. It can sometimes consist of numbers such as rating of pain from 1 to 10, but the numbers are not a measurement of a value but rather represent a specific cate

Measures of Central Tendency

Include various methods of representing the "middle" of the data set. Provide a quick summary by indentifying the central position of values within a data set. This includes mean, median, and mode.

Mean

Is also called the average. It cannot be used as a measure of cental tendency in all data sets. Only appropriate for interval or ratio data.

Median

The middle values once all values have been placed in order of magnitude. For data sets with an odd number of values, the median is simply the middle value. When a data set contains an even number of values, the median is the average of the two middle val

Mode

The value that occurs most often for a variable in a data set. The mode is the only measure of central tendency that is appropriate to use with nominal data. (nominal = unordered categories)

Measure of Dispersion

Describe how closely clumped together or widely spread apart the values are within a data set. Three most commonly used measures of dispersion are range, inter-quartile range, and standard deviation.

Range

Is calculated by subtracting the value of smallest magnitude from the value of greatest magnitude. A large range indicates a greater amount of dispersion amongst the data points, while a small range suggests data that are clumped toward a cental value.

Inter-Quartile Range

Is calculated by subtracting the value of the first quartile fromm that of the third quartile. This provides a summary of the amount of dispersion present in the middle half of the data. (percents)

Standard Deviation

Measure of the dispersion of values in a data set, which is expressed in the same units as the values themselves. It takes into account and assesses how far values are from the mean value. The difference between each value in the data set and the mean is