Averages and Range

Fundamental Definitions in Data Analysis

Data is defined as a set of information collected for study, reference, or analysis. Within any given data set, each individual piece of information is called a value.

Measures of Central Tendency

Measures of central tendency describe the center or typical value of a data set. Three standard measures are the mode, the median, and the mean.

The mode is the most common value present in a data set. It corresponds to the observation that appears with the greatest frequency.

The median is the middle value when the data is written in order. To locate the median, all values in the data set must first be arranged sequentially.

The mean is calculated as the sum of the values divided by the number of the values in the set. Expressed mathematically:

$\text{Mean} = \frac{\text{Sum of the values}}{\text{Number of the values}}$

Measure of Spread: Range

The range measures how spread out the values in a data set are. It is defined as the difference between the smallest and largest values:

$\text{Range} = \text{Largest value} - \text{Smallest value}$

The larger the range, the more spread out the values are across the data set.

Ordering Data

Arranging values in a consistent sequence is necessary for calculating statistical measures like the median. Data can be ordered in two directions:

Ascending order means arranging values from the smallest to the largest.

Descending order means arranging values from the largest to the smallest.