Saturday 4 March 2017

Fundamentals of Statistics

Sir Arthur Lyon Bowley
Sir Arthur Lyon Bowley


In the simplest form, Statistics is defined as a numerical representation of information. According to a renowned English statistician Sir Arthur Lyon Bowley, statistics refers to numerical statements of facts in any area of inquiry.

Sir Arthur Lyon Bowley, also an economist, worked on economic statistics and pioneered the use of sampling techniques in social surveys.

Statistics is also seen a branch of mathematics which deals with enumeration data (one type of numerical data). Statistics is used as a tool in data analysis of a research; it is used to gather, organize, analyze, and interpret information gathered.

Let’s first understand what the data is. Data refers to a set or a bundle of information which is collected in order to conduct a research. Data is of two types: Numerical, and Non-numerical.

The data that can be counted is termed as numerical data; it deals with numbers and calculation, whereas non-numerical data deals with information which cannot be counted rather it is inferred or assumed.

Though both types of data (numerical as well as non-numerical) are information, the role of statistics is confined to “numerical data” only.

Numerical data is of two types—enumeration data, and metric data. Enumeration data refers to information which can be counted, for example, class intervals, frequencies, etc. Metric data is based on measurement; it needs unit specification in order to make sense of data.

Branch of Statistics:

Descriptive and Inferential Statistics

There are two major branches of statistics—“Descriptive Statistics”, and “Inferential Statistics”.

Descriptive Statistics

It describes certain characteristics of a group of data. It has to be precise (precise means brief and exact). It limits generalization to the particular group of individuals observed. Hence, no conclusions are extended beyond this group, and any similarity to those outside the group cannot be assumed. The data describe one group and that group only.

Inferential Statistics

It is related to the estimation or prediction based on certain evidence. It always involves the process of sampling and the selection of a small group. This small group is assumed to be related to the population from which it has been taken. The small group is known as the sample, and the large group is the population. Inferential Statistics allows the research to draw conclusions about populations based on observations of samples.

Following are the two important goals of inferential statistics:

·         The first goal is to determine what might be happening in a population based on a sample of the population.
·         And the second goal is to determine what might happen in future.
Thus, inferential statistics are to estimate and/or to predict. In order to use inferential statistics, only a sample of the population is required.

Organization of Data:

Ordered Array

It refers to the data (a set of information) which is arranged in descending order, for example, 90, 80, 75, 68, 60. The Ordered Array, also known as Set, provides a more convenient arrangement. The highest score is 90 and lowest score is 60 are easily identified. In this way, the range (the difference between the highest and the lowest scores, plus one) can be easily determined.

Grouped Data

The data which can be presented in the form of class interval and frequency is known as the Grouped Data. In this way of presentation, the data are often more clearly presented. Data can be presented in frequency table with different class intervals, depending on the number and range of the scores. There is no rule that rigidly determines the proper score interval. However, intervals of 10 are frequently used.