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.

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.