Question

⦁   What is the interpretation of the value of the mean taken over a dichotomous variable, such as gender (where the value assigned to women in the sample is 1 and the value assigned to men in the sample is 0)?
⦁   Which of the following statistics are not sensitive to changes in a small number of values within the distribution: mean, median, range, interquartile range, variance?
⦁   Intuitively, what is the standard deviation measuring in terms of characterizing the spread of the distribution?
⦁   Under what circumstances is it more useful to apply the skewness ratio formula instead of the skewness formula?

Answer 1

(1) The mean taken over a dichotomous variable will fail to generate a meaningful interpretation. Because a variable like gender which is dichotomous in nature is actually a categorical data and mean can not be useful for such type of data. One may use proportions for drawing meaningful inference from such data.

(2) Among the given statistics variance is not sensitive to changes in a small number of values within the distribution.

(3) In measuring the spread of the distribution the calculation of standard deviation measures the characteristic in the follwoing manner -

If value of standard deviation is more it indicates that the spread of the distubion is large

If value of the standard deviation is less it indicates the spread of the distribution is small.

(4) When the value of mean, median and standard deviation for the distribution is given then one can use skewness ratio formula over skewness formula.

skewness formula is prefered when only the dataset of the distribution is available.