Introduction to Statistics
The study of data collection, organization, analysis, and interpretation is known as statistics. A statistical question is one for which there is no single answer. Instead, you can anticipate a variety of responses and are curious about their distribution and trends.
What is Statistics in Math?
Definition: Statistics is the branch of mathematics that deals with the gathering, organizing, analyzing, interpreting, and presenting of data. It is customary to start with a statistical population or a statistical model to be studied when applying statistics to a scientific, industrial, or social problem.
Identifying Statistical Questions
A statistical question is one that can be answered by collecting data from different sources. For instance, “How old am I?” is not a statistical question, whereas, “How old are the students in my university?” is a statistical question.
But don’t get confused between a survey question and a statistical question.
For example, a statistical question is “How many students of grade 6 have passed in Math?”
However in a survey question we are not going to ask people “How many students of grade 6 have passed in Math?” instead we ask “What is the grade that you have obtained in Math?” to each student of grade 6. So even though this is not a statistical question, it will help us to get the data to answer a statistical question.
Therefore a survey is the process of helping us collect and analyze data from the population.
Solved Examples of Statistics
Example 1: Identify the given problem whether it is statistical or not.
(a) What are the heights of the employees in your company?
(b) What is your name?
Solution:
(a) We can organize a survey inside the office and find the height of the employees. So, it’s a statistical question.
(b) My name is Aiden. So, it’s not a statistical question.
Example 2: The below-given dot plot shows the times of cars in a knockout race.
Part (a) On the dot plot, find and interpret the number of data values.
Solution: On the dot plot, there are 20 data values.
Part (b) How will you gather this information? What are the measurements in units?
Solution: A time dot plot can be used to collect this information and the time is measured in seconds.
Part (c) Construct a statistical question to which the dot plot can provide an answer. Then respond to the question.
Solution: One possible statistical question is “What is the time of arrival of the maximum number of cars?”
The time for the maximum arrival of cars is at 13.8 seconds.
Example 3: “What is the mass of a typical rabbit?” your teacher inquires. On a set of house rabbits, you conduct a science experiment. Answer the question with the information provided to you in the table.
Solution: You’re familiar with the herds of several rabbits. You must use the information to answer a statistical question.
Use a dot plot to visualize the data. Identify any data clusters, peaks, or gaps. Then, to answer the question, use the data distribution. Make a number line with the lowest value, 2, and the highest value, 9, on it. Then, for each data value, draw a dot above the number line.
The two major areas of statistics are descriptive statistics, which describes the properties of sample and population data, and inferential statistics, which uses those properties to test hypotheses and draw conclusions.
Statistics is the science and in some ways, the art of deriving knowledge from data. It is concerned with the gathering, analysis, and interpretation of data, as well as the effective communication and presentation of data-based results.
Sir Ronald Aylmer Fisher was a British statistician and geneticist, and is regarded as the father of statistics for his great contribution to this branch of mathematics