There are several laws and limitations in statistics. There is also a lot of distrust of statistics. Today, we will talk about the various laws of statistics, their limitations and distrust of statistics.

**Table of content**

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## Laws of Statistics

There are two laws of statistics which form the basis of the theory of sampling. These are:

- The Law of Statistical Regularity
- Law of Inertia of Large Numbers

### The Law of Statistical Regularity

This law forms the basis of the theory of probability in statistics. According to this theory, if you take a large random sample from a population, then it is fairly representative of the population.

According to **Prof. W.I. King**, “*The law of statistical regularity formulated in a mathematical theory of probability lays down that a moderately large number of items chosen at random from a very large group are almost sure on the average to have the characteristics of the large group.*” This law holds good if it meets two conditions:

- The sample is random
- The size of the sample is large

**Browse more Topics under Descriptive Statistics**

- Definition and Characteristics of Statistics
- Stages of Statistical Enquiry
- Importance and Functions of Statistics
- Nature of Statistics – Science or Art?
- Application of Statistics
- Meaning and Types of Data
- Methods of Collecting Data
- Census
- Sample Investigation
- Classification of Data
- Tabulation of Data
- Frequency Distribution of Data
- Diagrammatic Presentation of Data
- Graphic Presentation of Data
- Measures of Central Tendency
- Mean Median Mode
- Measures of Dispersion
- Standard Deviation
- Variance Analysis

### The Law of Inertia of Large Numbers

This law is the corollary of the law of statistical regularity. According to this law, a larger sized sample produces more accurate results. This is because large numbers have more stability, consistency, and steadiness as compared to small numbers.

## Limitations of Statistics

Despite its immense use, Statistics has many limitations. These are as follows:

### Deals in Quantitative Data

Statistics deals only with quantitative data and not the qualitative and descriptive facts like efficiency, intelligence, honesty, blindness, etc.

### Studies Groups not Individuals

Statistics does not deal with individuals but with groups. This is one of the biggest limitations of statistics. To give you an example, the income of an individual or profit of a particular business unit is not statistics since those figures are unrelated and incomparable.

On the other hand, the aggregate of figures relating to prices and consumption of various commodities and over varying time periods are statistics.

### Statistics is an inexact science

Statistical laws are not exact. In fact, the results are true only on averages. Also, they are valid only under a certain set of assumptions. Therefore, the science of statistics is less exact than natural sciences like physics, chemistry, etc.

### Misuse

Statistics deal with figures which are innocent in themselves and can be easily manipulated or distorted by people for their selfish motives. Therefore, it is a dangerous tool in the hands of a non-expert.

It is hence important that the user of the statistical methods has sound knowledge of the subject along with the self-control of an artist.

According to Prof. W.I. King, “*Statistics are like clay from which you can make a God or a devil as you please.*” He also said that “*The science of statistics is the useful servant but only of great values to those who understand its proper use.*”

## Distrust of Statistics

By definition, distrust means a lack of confidence or belief. Further, the science of statistics is always subject to doubt and suspicion because of its misuse by unscrupulous elements for their selfish motives. The common beliefs about statistics are:

- One ounce of truth can produce tonnes of statistics
- Statistics can prove anything
- It can prove nothing
- Figures don’t lie; cheater make figures up
- There are three types of lies – lies, damn lies, and statistics
- Numbers, though accurate, are open to manipulation by selfish people to conceal the truth and present a distorted picture of the facts.

Therefore, it is important to understand that statistics is a tool, which if misused can cause a disaster. Statistics neither approves or disapproves anything. Hence, you must take utmost care and precaution while interpreting statistical data in all manifestations.

## Solved Question

**Q1. Which two laws of statistics form the basis of the theory of sampling?**

Answer: The two laws of statistics which form the basis of the theory of sampling are:

- The Law of Statistical Regularity
- Law of Inertia of Large Numbers