Calculate Sample Variance of Given Numbers

Calculate the variance of the sample given the numbers 6, 9, 14, 10, 5, 8, and 11.

Variance is a measure of how much values in a data set deviate from the mean. It quantifies the spread of the data points. In this problem, you are tasked with calculating the sample variance, which can be slightly different from population variance due to the Bessel's correction. The Bessel's correction involves dividing by n-1 (where n is the sample size) instead of n, correcting the bias in the estimation of the population variance from a sample. Remembering this distinction can help in accurately calculating the sample variance and understanding the underlying data variability.

When calculating variance, the first step is to determine the mean of the sample. Once the mean is calculated, subtract the mean from each data point to find the deviation of each point from the mean. Then, square these deviations to remove any negative values, ensuring that variability in both directions is accounted for. Summing these squared deviations and then dividing by the sample size minus one gives you the sample variance. This method highlights the importance of understanding and applying key statistical concepts like mean, deviation, and variance to measure data dispersion effectively. Such skills are fundamental in statistical analysis and are widely used in various real-world applications to draw meaningful insights from data.