# Summarizing Data

## Measuring Spread: the Range

When datasets are large, it's important to find a smaller set of values able to describe its overall behavior.
The first indicator is the is

*of the dataset, that we obtain by subtracting its lowest value from its highest value. The range describes how spread are data.***range***Example*: The range of the set## Measuring the Central Tendency: the Averages

The

*(averages) summarize a dataset using one calculated value, that conveys information about the typical values of data and their distribution. The most common***measures of central tendency***of a dataset are the (***measures of central tendency***arithmetic*)*, the***mean***and the***median***.***mode**## Mean

The (arithmetic) is
is not defined.

*is the sum of all values in the dataset, divided by their number. If the dataset contains***mean***qualitative data*, it's not possible to calculate the mean of these data.*Example 1*: The mean of the set*Example 2*: The mean of the set## Median

The .
- The set contains 11 values (odd)
- Sort values in increasing order:
- The median is , that is the middle element of the list above.
- The set is already ordered, and contains 6 values (even)
- The values in the middle of the list are
- The median of the given set is the mean of these values:
is not defined.

*is the middle value of an ordered dataset, with data arranged in increasing order. - If the ordered data set contains an***median****number of values, the***odd**will be the***median***in the list. - If the ordered data set contains an***middle value***number of values, the***even***will be the (arithmetic)***median***of the two middle values. If the dataset contains***mean***, it's not possible to calculate the median of these data.***qualitative data***Example*1: Calculate the median of the set*Example*2: Calculate the median of the set*Example*3: The median of the set## Mode

The is .
has two modes: and .
is .

*is the value with the highest frequency in a dataset (i.e. that occurs most often) It is not necessarily unique, and it is defined also for qualitative datasets.***mode***Example*1: The mode of the set*Example*2: The set*Example*3: The mode of the set## New Resources

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