## WHAT ARE STATISTICS PROBLEMS?

The procedure of collecting and analysing the numerical data is called statistics. It makes the data interpretation and analysis easier and helps draw out significant conclusions from the given data. It is a concept that helps in effective management of numerical data as well as its representation in a presentable manner. Statistics has become a powerful tool in today’s industrial and capitalist society. Problems in statistics related data processing help in building statistical temperament within individuals. They gain relevant knowledge and skills in the concerned field and are prepared to deal with real world statistical data.

## HOW TO APPROACH **STATISTIC PROBLEMS**?

Statistical problems should be approached with an analytical mindset. Ultimately designed to draw out conclusive information for the future business or planning purposes. These are the exemplary situations that the individuals are bound to encounter in the field of data analysis and statistical management. Individuals can keep in mind the following points while solving statistical problems:

- Data should be copied carefully
- Data operations should be precise
- There should be accuracy in the interpretation
- Data analysis should be based only on the authentically collected data

## KEY POINTS TO REMEMBER BY SOLVING STATISTICS PROBLEMS

While solving statistics problems individuals should keep in mind certain key points that will help them in getting the job done. Statistics is a scientific process based on pre designed methods and is helpful in getting desired output effortlessly. The following points are elemental in solving statistics problems:

- Statistics is more than just numbers; it is a set of carefully collected data and should be dealt with likewise.
- Before operating on data, an appropriate method should be chosen that suits best to the data set.
- The different basic methods of data operation are sample size determination, standard deviation, mean, hypothesis testing and regression.
- The most commonly used technique because of its applicability to a wider range of datasets is multiple regression analysis.
- The basic four steps should be followed while dealing with the data, viz. interpreting the question well, collecting and organising data in a meaningful manner, performing appropriate operations and carefully drawing out conclusions.

## EXEMPLARY STATISTICS PROBLEMS

To get a general idea, a few statistics problems are given below that can be attempted by individual learners. Performing analysis on the below questions will be an easy task and the learners can get conceptual clarity by doing so.

**Problem 1**

Given below are three data sets A, B, and C.

A = {10, 11, 13, 7, 8}

B = {1, 10, 19, 1, 19}

C = {10, 10, 10}

a) Determine the mean of each data set.

b) Determine each data set’s standard deviation.

c) Which of the following sets has the greatest standard deviation?

d) Can you answer question c) without calculating the standard deviation?

**Problem 2**

There is a mean and a standard deviation for each data set.

a) What will be the new mean and standard deviation figures if the same constant k is applied to every data value in the above set? Explain.

b) What are the new mean and standard deviation values if each data value in the set is multiplied by the same constant k? Explain.

**Problem 3**

What can we say about the data values included in a given data set if the standard deviation is equal to zero?

**Problem 4**

The frequency table of 9 people’s monthly salaries is shown below.

a) Determine the average of the 9 people’s salaries.

b) Determine the standard deviation of the 9 people’s salaries.

Salary (in Rs) | frequency |

3000 | 4 |

4200 | 5 |

4800 | 8 |

These are some of the very basic problems and can be easily solved. Learners can get themselves evaluated by anyone having basic knowledge of statistics at home or outside, by their friends.

## HOW TO SCORE BROWNIE POINTS?

In statistics one can master the art of data analysis by going through following simple steps.

**Consistent practice**: one can master statistics only when they have explored sufficient number questions and experienced problem solving in all the dimensions of a given topic.

**Joint study groups**: when one gets to interact with people from diverse walks, they are exposed to new techniques that are adopted by those individuals. These strategies can sometimes be better than one’s own strategies and can be helpful in increasing one’s score.

**Question interpretation**: even if someone is 100% confident in his/ her skills they should definitely be highly attentive in reading and understanding the question. This should be done to avoid unexpected loss of marks. One should carefully read and interpret the question.

**Mistakes**: repetition of same mistakes should be checked immediately as soon as they are discovered. This makes sure that not even a single mark is lost. All the brownies come to the determination.**Revision**: Constant revision is the key. There are no words that can justify the significance of revision. Revision is a must in statistics. All the important formulae, methods and tricks should be repeatedly revised. This consolidates them in mind and can be easily recalled while encountering a problem.

## THE BOTTOM LINE

Statistics is all about practice. One should learn the basics and solve as many problems as possible. This is the only key to solving statistics problems. These are generally at an average level of difficulty. Some problems might be a little hard to solve but most of the problems can be solved with the overall knowledge of concepts. Apart from this students should stick to consistent revision of all the topics and try to solve their common mistakes. They should focus more on weak points and get themselves regularly evaluated in order to score good grades.