Question

Give an example of a study where it would be more appropriate to report the standard deviation rather than the interquartile range. Explain why the standard deviation is the better choice.

Answer 1

The standard deviation plays a central role in statistics for two reasons:

1)it is a key factor in the central limit theorem (which explains to students why increasing the sample size of a data set should give us a "better" estimate for the mean)

2) and also because it gives us the variance (which is fundamental for such methods as ANOVA, linear regression, etc).

However, one use of the standard deviation that is very important for beginning students to understand is that for the normal distribution, we actually think of the SD as a measuring stick that helps us tell how likely an even is to occur (i.e. the all important "68–95–99.7 rule").

interquartile range is preferred when the data are skewed or have outliers. An advantage of the standard deviation is that it uses all the observations in its computation.Your answer is correct.D.The interquartile range is preferred when the distribution is symmetric. An advantage of the standard deviation is that it increases as the dispersion of the data increases.E.The interquartile range is preferred when the data are not skewed or no have outliers. An advantage of the standard deviation is that it uses all the observations in its computation.F.The interquartile range is preferred when the data are bell shaped. An advantage of the standard deviation is that it increases as the dispersion of the data increases.

An example

Consider 2 hypothetical job offers: one is in city A, located in rural area where the salary ~ N(30K,5K) and the other is in city B, a large city where salary ~N(60K,10K). Suppose that salary offer from city A is 45K and the salary offer from city B is 60K, which should you choose? Here simply looking at how far the salary offers from the means in units of SD, tells us that city A is the better offer.

Moreover, the IQR is preferred when the data are not skewed or no have outliers. An advantage of the standard deviation is that it uses all the observations in its computation.

Standard deviation is considered to be the best measure of dispersion and is thereore, the most widely used measure of dispersion. (i) It is based on all values and thus, provides information about the complete series. Because of this reason, a change in even one value affects the value of standard deviation.