Statistics is the science of analyzing data. When you are presented with the daily closing prices of a stock for the past one year, how do you make sense of this data? Using the tools and techniques offered by statistics, you can analyse the data in various ways. For example, you can find out the average price of the stock over the past one year. You can also calculate other statistics such as the dispersion of the stock prices around the mean. Statistics deals with all aspects of data including collecting data, organizing data, analysing it, interpreting it and presenting it in a useful forms.
All statistical methods can be classified as descriptive or inferential statistics.
Descriptive statistics refers to analysis of data in order to summarize the important characteristics of data in a meaningful way. However, descriptive statistics does not allow us to make any conclusions beyond the data. Two important types of descriptive statistics include the Measures of Central Tendency and Measures of Dispersion. For example, you may have the monthly savings data of 100 families and using that you can calculate descriptive statistics such as average savings and the dispersion of savings in this group of 100 families. However, descriptive statistics will describe the characteristics of only this group of 100 families. This group of data that contains all the data that you are interested in describing is called population. Another example of population is the returns of all stocks trading on NASDAQ. Note that the size of the population does not matter. As long as the data set, whether small or big, contains all the data that you are interested in, it represents your population.
Inferential statistics uses the sample data to reach some conclusion about the characteristics of the larger population. Using the same example of savings by families, we know that descriptive statistics cannot be used to make any conclusions about any families other that the 100 families in our data group. For example, what if you were interested in the savings pattern of an entire country, such as the U.S. It may not be feasible or practical to collect the monthly savings data of every family in the U.S. that constitutes your population. In that case, you will take a small sample of families from across the U.S. that will be used to represent the larger population of U.S. You will use this sample data to calculate its mean and standard deviation. We use inferential statistics techniques to make conclusions or inferences about the population that the sample represents. Two common methods of inferential statistics are Estimation of Parameters, and Hypothesis Testing.