Descriptive Measures of Quantitative Data

Descriptive statistics measure central tendency, dispersion, and distribution. I exemplify these measures from the daily database on COVID-19 incidence worldwide as of April 29, 2020, which I downloaded from the European Centre for Disease Prevention and Control website. The dataset has 109 daily records.

Measure of Central Tendency

Mean incidence per day is 28,016.6 persons. Median or second quartile is located at 3,907 persons and mode is 17 persons infected in a day. Mean, median, and mode are equal for normal distribution. Both median and mode are less than mean indicating that the dataset is distorted from normality.

Measure of Dispersion

Range of 101,727 is very wide between a maximum of 101,728 persons to one person infected on a single day worldwide. The standard deviation is calculated at 34,079.4 persons. For the normal distribution, 95 percent of the data values fall within two standard deviations from the mean. In this dataset, 95 percent of data values fall within plus 96,175.4 to minus 40,142.2. 

Measures of Distribution

Skewness value is positive 0.73.  A normal distribution has zero skewness. The standard error of skewness is 0.23. The positive value indicates that the distribution is positively skewed with a right tail. Since a skewness value is more than two times its standard error the distribution is asymmetric.

Kurtosis value is negative 1.24. A normal distribution has a kurtosis value of zero. The standard error of kurtosis is 0.45. The negative value indicates that the distribution is flatter than normal with the data values less clustered around the center of the distribution, which is also referred to as platykurtic distribution. Since a kurtosis value is more than two times its standard error the distribution is abnormal.

In a nutshell, descriptive statistics measure the central tendency, variability, and distribution of data. The given dataset is positively skewed and flatly distributed than normal.