Mean and variance

Introduction to Mean and Variance

• In statistics, the mean is the average of a set of data points. It provides a measure of the central tendency of the data.
• Variance is a measure of “spread,” that is, how far each data point in a set is from the mean.

Calculating the Mean

• To calculate the mean, add together all of the data points and divide by the number of data points. This is known as the arithmetic mean.

Calculating Variance

• Variance is calculated by taking the average of the squares of the differences between each data point and the mean.
• More specifically, to calculate the variance: 1) Subtract the mean from each data point to get the difference. 2) Square each difference. 3) Find the average of these squared differences.

Properties of Mean and Variance

• The mean is influenced by every data point in the set. If one data point changes, the mean changes.
• Variance gives more weight to outliers (data points far away from the mean) because it squares the differences. As a result, one large outlier can significantly increase the variance.

Interpreting Mean and Variance

• A higher variance indicates a greater spread in the data. If the variance is small, it suggests that the data points are generally close to the mean.
• The units of variance are the square of the units of the original data. For example, if your data is in metres, the variance would be in square metres.

Further Points

• Mean and variance are fundamental concepts for many statistical methods and are crucial for the Further Stats 1 syllabus.
• Understanding the concepts of mean and variance is vital for performing statistical analyses and understanding their results.