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The standard deviation is a key measure used to quantify the amount of variation or dispersion in a set of data values. It's a statistic that indicates how each number in a dataset deviates from the mean, or average, value of the dataset.
Calculating the standard deviation involves the following steps:

• Find the mean (average) of the dataset.
• Subtract the mean from each data point and square the result.
• Calculate the mean of these squared differences.
• Take the square root of this mean. This result is the standard deviation.

The larger the standard deviation, the more spread out the values in the dataset are. For example, in the exercise, construction workers have a standard deviation of 2.3, meaning their number of missed days varies more than the factory workers, who have a standard deviation of 1.8. However, when comparing variability between datasets with different means, it's better to use another measure called the coefficient of variation.

The coefficient of variation (CV) is a statistical measure that helps to understand the degree of variability in data compared to its mean. It is especially useful when the means of the datasets are significantly different. This is because CV normalizes variability by expressing it as a percentage of the mean, allowing for a direct comparison of variability across datasets.
To calculate the CV, use the formula:

• CV = (Standard Deviation / Mean) × 100%

In the exercise, the CV for the construction workers is calculated as approximately 20.91%, while the CV for the factory workers is about 22.50%.
A higher CV value signifies greater relative variability. In this case, factory workers have a slightly higher CV, indicating that, relative to their mean, their attendance variability is higher than that of the construction workers.

When comparing datasets, the mean provides a central value that reflects the average of the dataset. Although it is not a direct measure of variability, it is crucial when using methods like the coefficient of variation, where the mean is part of the calculation.
In the exercise, the mean for construction workers is 11 days missed per year, while for factory workers it is 8 days missed per year. These different means show that, on average, construction workers miss more days. However, just comparing average days missed doesn't tell us about the relative variability of those days. That's why CV is used to take the mean into account when assessing variability. In conclusion, while the mean provides helpful information about the central tendency of the data, it should be used alongside other statistical measures to fully understand data variability.