Question

a. What is an example of when you would want consistent data and, therefore, a small standard deviation? b. What is an example of when you might want a large standard deviation? That is, data that is more spread out?

Answer 1

Answer:

1.(a). Consistency of data can be viewed in many ways .Typical measures of data consistency include statistics such as the range (i.e., the largest value minus the smallest value among a distribution of data), the variance (i.e., the sum of the squared deviations of each value in a distribution from the mean value in a distribution divided by the number of values in a distribution) and the standard deviation (i.e., the square root of the variance).

A data with small standard deviation is called a consistent data( in terms of standard deviation).

Example of consistent data:

• A weather reporter is analyzing the high temperature forecasted for a series of dates versus the actual high temperature recorded on each date. A low standard deviation would show a reliable weather forecast.

1.(b). Example of data with high standard deviation:

• A dog walker wants to determine if the dogs on his route are close in weight or not close in weight. He takes the average of the weight of all ten dogs. He then calculates the variance, and then the standard deviation. His standard deviation is extremely high. This suggests that the dogs are of many various weights, or that he has a few dogs whose weights are outliers that are skewing the data.​​​​​​​​​​​​​​