# Quartiles and Standard Deviation

## Quartiles and Standard Deviation

# Quartiles

**Quartiles**are values that divide a dataset into four equal parts, or quarters.- The
**first quartile (Q1)**, also known as the lower quartile, is the value below which 25% of the data falls. - The
**second quartile (Q2)**is the median, below which 50% of the data falls. It also divides the lower and upper quartiles. - The
**third quartile (Q3)**, also known as the upper quartile, is the value below which 75% of the data falls. - Quartiles can help give a clearer picture of the distribution of a dataset, especially when you’re dealing with large datasets.
- The
**interquartile range (IQR)**is the range within which the middle 50% of a dataset falls, and is calculated as Q3 - Q1. - The IQR is a useful tool for spotting outliers. Data points that fall more than 1.5 times the IQR below Q1 or above Q3 are considered outliers.

# Standard Deviation

- The
**standard deviation**is a measure of the amount of variation or dispersion within a set of values. - A low standard deviation means that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
- To calculate the standard deviation, first calculate the mean of the dataset.
- Then, subtract the mean from each number in the dataset and square the result. This gives you a list of ‘squared differences’.
- The mean of these squared differences is known as the
**variance**. - The standard deviation is the square root of the variance.
- Understanding standard deviation can give valuable insight into how consistent or reliable a set of data is. It is used in a range of fields, including finance, engineering, and physics.
- The symbol for standard deviation is σ (sigma) when referring to population standard deviation, and s when referring to sample standard deviation. Be familiar with both.