Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of data. Statistics is applied in a large variety of disciplines including humanities, business, science and government, and even sports. We come across statistics in all walks of life on a daily basis. Scientific results are often published in the form of statistical data. The same is true for governmental reports and business numbers. News reports are often based on statistical data. Even in our daily conversations, we often talk about averages and mean. However, it is important to remember that statistics conceal as much as they tell.
Unfortunately, almost all the information we receive is in the form of some or other statistics. Popular culture trains us from early childhood to trust statistics blindly. Many of us do not even realize that mean and median are not the same. When a report says that something has increased or decreased by a certain percentage, how many of us stop to analyze what it exactly means. For example, when a news report says that inflation has risen to 3%, how many of us realize what it really means. And why is it worse than an inflation rate of, say 1.5%? We have to realize that whether the inflation rate is 1.5% or 3%, the prices are rising in both cases. The only difference is the rate of this price rise. Unfortunately, many of us do not realize this simple fact and react with panic at a news report stating that the rate of inflation has risen. Stock markets fall and the common man begins to hoard items of daily use in anticipation of unprecedented price rise simply because a news report has stated that inflation has risen to an 11 year high.
Understanding statistics requires what is known as statistical literacy. When newspaper reports present a statistical fact, they often do not mention the statistical method used to come at the data. To properly understand statistical information it is important to know the origin of the data, sample size, and the reliability of the reported data. Next, it is important to evaluate, based on this information, if the claims made by the report make statistical sense and if there are any alternative interpretations possible.
Descriptive Statistics
In Descriptive Statistics, the emphasis is on analyzing observed measurements. Descriptive Statistics tries to answer questions such as what is the typical value of the measurements of a population, what is the variation and distribution of the measurements, the extreme values in the population, and the relationship between the different variables.
With descriptive statistics, different statistical techniques are used in different situations and there are no set rules as to what technique should be used in any particular situation. As a result, the application of descriptive statistics can raise more questions than answers. For example, if a statistic states the median age of a class, we still do not know the ages of the youngest and oldest students. The average age of the class also does not answer that question. The range of the ages of the students of a class can tell us the ages of the youngest and the oldest student, but it does not tell us the age of the maximum number of students of the class. However, descriptive statistics helps us comprehend very large sets of data were inspecting the individual component of the data can be extremely difficult.
Inferential Statistics
While descriptive statistics deals with the entire population, inferential statistics deals with a sample. It would be ideal if we could always measure the entire population to arrive at statistical data. Unfortunately, this is not always possible. For example, it is not possible to interview each and every British subject during elections to find out how they intend to vote. Under the circumstance, experts carry out a poll of a sample and based on the results of this sample try to predict the results of the election. This is inferential statistics, that is, it tries to infer the voting trends of an entire population based on the data available from a sample. In other words, in inferential statistics, we try to reach a conclusion about an entire population based on the data available from a sample of the population.
Uses of Statistics
Statistics is used in four different ways by us. Statistics is a subject we study; it is a method used to study data; it is also a collection of data and has specific uses such as calculating averages.
As a subject, statistics cover a wide range of concepts. In descriptive statistics, it measures the center of data which is expressed as mean, median, or mode. It also gives frequency distribution. Statistics also calculates the range, variance, and standard deviation. But when we move beyond this basic statistics, we realize that statistics also covers a whole range of topics that cannot be completely grasped even with a Masters’s degree in the subject. Some of the topics which are included in statistics are probability, regression, inference, and model building, analysis of variance, and relationship in qualitative.
As a method used to study data, statistics have proven to be an extremely useful tool. Raw data when presented without performing any statistical calculations on it can be extremely cumbersome and difficult to comprehend. For example, a survey of the number of hours the families of a community watch television would give a huge volume of data but this data would be incomprehensible to most people until it is presented in a proper format, most probably as a graph. When presented as a graph, any person can easily understand the television viewing habits of the community at a single glance.
While graphs are useful to get a snapshot of data, sometimes, it is necessary to get the raw data in order to be able to make a proper analysis. Once again, this data needs to be presented in a format so that it is easily comprehended. For example, a survey is often carried out by a person who ticks the answers on a piece of paper. However, if these pieces of paper were presented to the management of a company, they would be totally useless. The data collected in the survey needs to be tabulated so that a person can understand the findings of the survey. Finally, statistics have specific uses such as calculating averages, median, range, probability, etc.
When properly used, statistics can be a very useful tool. However, it must be kept in mind that depending upon the method used, statistics only presents one side of the picture. One would be grossly mistaken to take the presented data as gospel truth without trying to understand the mathematics behind it. While statistics do not actually lie, they can be quite misleading. So it is important to remember that statistical data must always be interpreted with caution.