Question

Assume you computed the mean height equal to 6 feet with a SD of 1 foot in a given sample. Heights between 5 and 7 feet are within one SD of the mean, and average in their deviation from the mean. Someone would have to be greater than 7 feet to be taller than average in this sample, and less than 5 feet to be shorter than average. The mean of the sample is not very useful because of the varied range of heights.

If the SD for height was 1 inch instead of 1 foot, then most people would score between 5"11 and 6'1", making a height of 6 feet a close estimate of the height of most people in the sample. The lower the SD, the less the scores differ from the mean, making it a relatively accurate measure.

Give an example of a value of a variable that is nearly average and one that is far above or below average. Explain your answer using the SD.

Give an example of a variable with a SD indicating an accurate mean and a SD indicating a less accurate mean.

Answer 1

Suppose we consider the variable with mean 6' and SD 1'. Then 5'10" is near average as it's distance from mean is lesser than 1 SD and 8' is far above than mean because it is 2 SD far from mean.

Suppose we consider a variable with mean 5 and SD 0.Then all values of this variable will be the mean which implies it will be an accurate mean.Now consider a variable with mean 5 and SD 5.Then any value between 0 and 10 would be closer to the mean which makes this variable a less accurate mean.