Question

This lesson asked you to investigate what it means for data to fall within 1, 2, and 3 standard deviations from the mean in a variety of normal distribution curves. Imagine that you hold a position on your city council and are in charge of creating new programs to benefit members of your community. In some cases, you must also decide which parts of the population are eligible for enrollment in a given program. How might the concept of standard deviations from the mean be interpreted in your decisions? For example, is it fair to make most programs only available to populations within 1 standard deviation from the mean? Can you imagine cases where you might want to create new programs for people who fall toward the extreme ends of the distribution? Give your opinion as well as some examples. ​

Answer 1

The data in statistics is generally supposed to deviate or vary from the mean. Standard deviations of 1, 2, and 3 are commonly used to calculate variability according to the empirical norm. In a normal distribution, we estimate 68 percent, 95 percent, and 98 percent of the data to be within 1, 2, and 3 standard deviations of the mean, respectively. This implies that the given percentage of data will lie within an interval of less than or greater than the standard deviation. If the values within a given standard deviation from the mean are standardized, the z value will always be equal to or less than the given standard deviation.

We should look at a program that aims to help people get out of poverty by using the standard deviation principle. The aim of the program is to provide free seeds to poor people who have been suffering from low yields due to the use of local seeds. If we use the definition of one standard deviation of the mean, or 2 and 3, we will favor the majority of people, but we will leave the poorest people in society behind.