Calculating Standard Deviation from a Data Set

Calculate the standard deviation of the numbers shown in the table below: 76, 84, 69, 92, and others to a total of 10 numbers with a sum of 800.

Calculating the standard deviation is a fundamental concept in statistics that quantifies the amount of variation or dispersion in a set of numbers. Here, the problem involves determining the standard deviation from a given data set. The first step in solving this problem is to understand that standard deviation is essentially the square root of the variance, which is the average of the squared differences from the mean.

To approach this, you first need to calculate the mean (average) of the data set, which in this instance is indirectly provided by the sum of the numbers. Once the mean is determined, the next step is to compute each data point's deviation from the mean, square each of these deviations, and then find the mean of these squared deviations. The square root of this result gives the standard deviation.

This problem provides a useful exercise in understanding how standard deviation functions as a measure of spread in a distribution, especially when dealing with smaller sets of data. It also emphasizes the role of each calculation step and how they contribute to assessing data variability. Such understanding is crucial for any statistical analysis, providing insights not just into central tendencies, but also into the reliability and variability in data outcomes.