Statistics as a field of knowledge proved so much in the world as a very powerful tool in almost all fields of work. Statistics can be found in the field of research, education, business, politics, psychology, and even in a simplest event that needs analysis. The New Encyclopedia Britannica defines Statistics as an art and science of gathering, analyzing, and making inferences from data.

It has been very useful in recording facts about people, objects, and events and in making predictions and decisions based on the available data. In this modern time, statistics plays a great role as a tool in gathering opinions from a survey. These opinions usually influence different sectors of society and help them anticipate possible solutions or actions they have to face. For example, in the case of a business, a company of a certain brand of product can do some innovations in terms of promotion, quality of the product or price once the survey shows negative feedback from the customer.

In this article, we are going to cover the key concepts of the Elementary along with the various types of questions, important formulas along with various tips and tricks. We have also added a few solved examples, which candidates will find beneficial in their exam preparation. Read the article thoroughly to clear all the doubts regarding the same.

History of Statistics & Its Modern Uses

One of the ways to appreciate what is being studied is to know its origin and how it developed and helped mankind. The history of statistics can be traced back at least to the 3500 years before the birth of Christ. Statistics had been used in Egypt in the form of recording the number of sheep or cattle owned, the amount of grain produced, and the number of people living in a particular city. In 700 BC, Roman Empires used statistics by conducting registration to record population for the purpose of collecting taxes.

Modern Statistics is said to have begun with John Graunt, an English tradesman. Graunt collected the bills of mortality that includes information about the numbers and causes death in the city of London. He analysed more than 50 years of data and created the first mortality table, a table which shows how long a person may be expected to live after reaching a certain age.

In modern times, statistical methods have been used to record and predict such things as birth and death rates, employment and inflation rates, sports achievements and other economic and social trends. In the age of information technology, a lot of computer programs such as Microstat, Soritec Sampler, SPSS and others are available which perform calculations in statistics.

When you’ve finished with Elementary Statistics, you can learn about Data Interpretation concepts in depth here!

What is Elementary Statistics?

The branch of mathematics in which we study about the collection, organization, analysis, interpretation and presentation of data (information) is referred to as Elementary Statistics.

Eg: the collection of children of different ages in a city, the collection of marks obtained by students in different subjects etc.

Let us now see the type of elementary questions candidates can expect in various competitive examinations.

Fields of Statistics

Statistics can be categorized into two main branches such as Descriptive Statistics & Inferential Statistics.

Descriptive Statistics, is concerned with the method of collecting, organizing, and presenting data appropriately and creatively to describe or access group characteristics.

Inferential Statistics, is concerned with inferring or drawing conclusions about the population based on pre selected elements of population.

How to perform Presentation of Data in Elementary Statistics 

We can present data in various forms like tables, graphs and diagrams.

(a) Presentation of Data in the form of a table 

Step 1: At first arrange the data in ascending or in descending order

Step 2: Make a box with the suitable number of rows and columns

Step 3: Fill the suitable headings in the 1st column and the 1st row

Step 4: At last fill the collected data in the box

(b) Presentation of Data in the form of bar graph

Step 1: At first draw axes (X-axis and Y-axis)

Step 2: Represent the variant or class interval on X- axis

Step 3:.Represent the frequency on Y- axis

Step 4: Place bars (rectangles) adjacent to each other as well as separated from each other such that the height of bars represent the frequencies of the respective observations.

(c) Presentation of Data in the form of pie chart

Step 1: At first draw a circle

Step 2: central angle = (frequency of an observation / total number of observation) x 360°

Use this formula to find the central angles of the observations.

Step 3: Make central angles by the help of compass

How to Measure the Central Tendency in Elementary Statistics 

(a) Mean 

The mean of a data is equal to the average of the data and it can be found by the help of the formula

(b) Median

The middle most observation of the data is called the Median of the data. We can find the median of a data by the help of some steps.

Step 1: At first arrange the given data in ascending or in descending order

Step 2: Count the number of observation

Step 3: When the number of observation (n) is odd, the median is the value of the

Step 4: When the number of observations (n) is even, the median is the value of the

(c) Mode

The mode is that value of the observation which occurs most frequently Mode of the data is denoted by M0

How to Solve Question Based on Elementary Statistics – Know all Tips and Tricks 

Candidates can find different tips and tricks from below for solving the questions related to Elementary Statistics.

Tip # 1: Variate – The quantity that we measure from observation to observation is called a Variate.

Eg: 1.5, 2, 2.5 etc. are called variates.

Tip # 2:Frequency – the number of observations of a particular variation of a class interval is called the frequency of that variate or interval.

Eg: 100 is the frequency of 3.5 years old children.

Tip # 3: Cumulative Frequency – It is the sum of frequencies of a class and all the classes below it.

Eg: in 2nd table 550 is the cumulative frequency of class 5 – 7

Tip # 4: Class Interval – the numerical width of any class in a particular observation is called the class interval.

Tip # 5: Lower Limit – the left end value of a particular class is called lower limit of that class.

Eg: in class interval 3 – 5, lower limit is equal to 3

Tip # 6: Upper Limit – The right end value of a particular class is called the upper limit of that class.

Eg: in class interval 3 – 5, upper limit is equal to 5

Tip # 7: Class Size – The difference between the upper limit and the lower limit of a particular class is called class size.

Eg: the width of above class intervals is 2.

Tip # 8: Class Mark – The mid value (average value) of a class interval is called the class mark of that class.

Tip # 9: Mode = 3 × Median – 2 × Mean, [M0 = 3 × M – 2 × X̅]

Elementary Statistics Sample Questions

Question 1: In a village 50 children are of 2 years old, 25 children are of 1.5 years old, 25 students are of 2.5 years old, 100 children are of 3.5 years old, 100 children are of 4 years old, 200 children are of 6 years old, 50 children are of 6.5 years old, 250 children are of 7.5 years old and 75 children are of 8 years old. Prepare a table of the above collection.

Solution:

It can also be presented in the form of classes and groups.

Question 2: Find the mode of the following marks out of 10 obtained by 15 students. 4, 3, 5, 6, 2, 5, 4, 7, 8, 9, 2, 4, 5, 6, 4

Solution: Marks of students in ascending order 2, 2, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9 Since, 4 occurs four times

So, the mode of this data is 4.

Question 3: The marks of 13 students in an examination are 55, 65, 72, 94, 64, 68, 54, 62, 58, 75, 80, 82, 60.

Solution: Marks of students in ascending order 54, 55, 58, 60, 62, 64, 65, 68, 72, 75, 80, 82, 94.

Since, the total number of observations is 13 (odd)

So we get median = 7th observation = 65

Question 4: Draw a line graph of the given data.

Solution: 

Question 5: Draw a pie chart of the given data.

Solution:

We hope you found this article regarding elementary statistics was informative and helpful, and please do not hesitate to contact us for any doubts or queries regarding the same. You can also download the Testbook App, which is absolutely free and start preparing for any government competitive examination by taking the mock tests before the examination to boost your preparation.