Descriptive statistical analysis

Question

I have some data obtained from questionnaire. The question asks to perform a descriptive statistical analysis for the above data and hence interpret your results. What does it mean? Is it mean I have to find the mean median mode standard deviation variance?

Answer 1

Before starting to do numerical and graphical descriptions of data for each question, it is important to determine whether the answers to the question are nominal, ordinal, or essentially numerical.

NUMERICAL (numbers, perhaps intervals): Perhaps age, income, or commute distance to work. Modal intervals should be obvious. It might be possible to estimate medians and ranges. Depending on allowed answers, perhaps even means and standard deviations. Graphical display might be a bar chart, showing the relative frequency of each interval.

ORDINAL: Answers like 'Strongly disagree/ disagree/ neutral/ agree/ strongly agree' or 'Never/ rarely/ occasionally/ often'. You should be able to find mode and median. Bar chart (with spaces separating bars) to make it clear you are not representing a continuous scale.

NOMINAL: Answers like 'Male/Female' or 'Catholic/ Protestant/ Jewish/ Muslim/ Hindu/ Buddist/ Other'. Categories have no natural order. Mode is the only valid measure of centrality. Pie chart or bar chart.

Here is a summary of which measures of centrality you can use of which data types.

 Valid Measures of Centrality for Various Data Types

           Nominal      Ordinal      Numerical
 Mean                  (See Note)       OK
 Median                    OK           OK
 Mode        OK            OK           OK 

Computing the mean required addition and division, these arithmetic procedures are only appropriate for numerical data. Finding the median requires sorting and picking the 'middle' value. Ordinal and numerical data can be sorted, Nominal cannot.

Note: Grades are inherently ordinal. Educational institutions customarily assign arbitrary numerical values to these, such as A = 4, B = 3, and so on. Then these numerical values are averaged to get a GPA for each student. (Are two C's really the same as an A and an F?) For large datasets the mean is a lot easier to find than the median. This practice of grade points originated in an era when it was feasible to compute GPAs, but not grade medians for large numbers of students. It is relatively easy to find the median of a dozen numbers, but sorting a thousand as a prelude to finding the median requires some computing power--power which is now routinely available. Even so, don't expect GPAs to disappear anytime soon.

'Likert' scaeles widely used in psychology and other social sciences are another (often problematic) kind of attempt to treat essentially ordinal data as numerical. (Can you meaningfully add 'Strongly opposed' and 'Favor'?)