The arithmetic mean (often simply called the mean) is calculated by summing all the values in a dataset and then dividing by the count of those values. It's a widely used measure but can be significantly influenced by extreme values (outliers) in the data. For example, if a company's salaries are mostly around $50,000 but one executive earns$1,000,000, the mean salary will be much higher than what most employees earn.

The median is the value that separates the higher half from the lower half of a data sample. To find the median, you first sort the data in ascending order. If there's an odd number of data points, the median is the middle value. If there's an even number, the median is the average of the two middle values. The median is a robust measure, meaning it's not as sensitive to extreme values as the mean.

The mode is the value that occurs most often in a dataset. A dataset can have one mode (unimodal), more than one mode (multimodal), or no mode at all if no value repeats. The mode is particularly useful for categorical data, such as customer preferences or product types, where calculating a mean or median might not be meaningful.

The range is the simplest measure of variability. It is calculated by subtracting the minimum value from the maximum value in a dataset. While easy to calculate, the range is highly sensitive to outliers and only uses two data points, providing a limited view of the overall spread.

Variance is a measure of how far a set of numbers is spread out from their average value. It is calculated as the average of the squared differences from the mean. Squaring the differences ensures that all values are positive and gives more weight to larger deviations. It's a key component in many statistical tests.

The standard deviation is the most commonly used measure of dispersion. It represents the typical amount that each data point deviates from the mean. A low standard deviation indicates that data points are generally close to the mean, while a high standard deviation indicates that data points are spread out over a wider range of values. It's often preferred over variance because it's in the same units as the original data.

Skewness quantifies the degree of asymmetry of a distribution. A perfectly symmetrical distribution, like a normal distribution, has a skewness of zero. If the tail on the right side of the distribution is longer or fatter than the left side, the distribution is said to be positively skewed (or right-skewed). In this case, the mean is typically greater than the median. Conversely, if the tail on the left side is longer or fatter, the distribution is negatively skewed (or left-skewed), and the mean is typically less than the median.

Kurtosis describes the shape of a distribution's tails relative to its peak. It indicates whether the data are heavy-tailed or light-tailed relative to a normal distribution. A distribution with high kurtosis (leptokurtic) has heavier tails and a sharper peak than a normal distribution, suggesting more extreme values. A distribution with low kurtosis (platykurtic) has lighter tails and a flatter peak, indicating fewer extreme values. A mesokurtic distribution, like the normal distribution, has kurtosis equal to that of the normal distribution (often defined as 3, or 0 when using excess kurtosis).