Question

You are planning to study for your statistics examination with a group of classmates, one of whom you particularly want to impress. This individual has volunteered to use statistical software to get the needed summary information, tables, and charts for a data set containing several numerical and categorical variables assigned by the professor for study purposes. This person contacts you about the printouts and exclaims: “I’ve got it all – the means, the medians, the standard deviations, the boxplots, the pie charts – for all our variables. The problem is, some of the printouts look weird like the boxplots for gender and for major and the pie charts for salary and for height. Also, I cannot understand why the professor said we can’t get the descriptive statistics for some of the variables – I got them for everything! See, the mean height is 68.3, the mean for salary is 54,327, the mean for gender is 1.5, and the mean for major is 4.6.” What is your reply?

Answer 1

EXPLANATION OF WHY DESCRIPTIVE STATISTICS IS NOT TO BE APPLIED FOR QUALITATIVE DATA SUCH AS GENDER,:

The Descriptive statistics, viz., (i) Measures of Central Tendency (Mean, median, Mode), (ii) Measures of Variation (Range, Mean Deviation, Standard Deviation, Variance), (iii) Skewness and (iv) Kurtosis are meaningful only for Quantitative Data, such as height, salary etc. For Qualitative Data such as gender, they are meaningless because of the following reason:

Qualitative data are categorical in type: Ordinal (variables have a natural ordered categories, such as Unhappy, Happy Very Happy) or nominal. (Labeling variables such as Gender: Male/ Female). THE QUALITATIVE DATA ARE NOT MATHEMATICALLY TRACTABLE; i.e., we cannot do mathematical operations with qualitative data and that is the reason Descriptive statistics have no meaning for Qualitative data.

Even assuming that we give numerical values to qualitative data, the results of the analysis will be meaningless as shown below:

Consider 4 Males and 5 Females. Let us give 1 for Male and 2 for female. Thus, we get the mean of the data as :[ (4X1) + (5 X 2) ]/2 = 14/2 = 7, which is meaningless.