Introduction to Statistics

There are two kinds of statistics, the kind you look up and the kind you make up. – Rex Stout, Death of a Doxy

Statistics is a process of collecting, analyzing, interpreting and statistical representation of data. It focuses on achieving information from numerical data. It can sum up and simplify large amounts of numerical data. This area focuses on applications and therefore, it is distinctively considered as a mathematical science. Statistics is used in various sectors related to psychology, geology, sociology, weather forecasting, probability and many others. The objective of Statistics is to gain understanding from data it focuses on applications and hence, it is distinctively measured as a Mathematical science. Modern data analysis forever involves graphical valuations of relationship. It becomes vital to understand and check before making statistical inferences.

Use of statistics in Real life

Statistics is all over the place, from election predictions to anything such as food product which says they x% more or less of an exact ingredient are a statistic. Life expectation is a statistic. If you play games for example card games; card counting utilizes statistics. There are tons of statistics all over the place you look.

Importance of Statistics

Statistics is not just a branch of mathematics but a complete subject in its own which studies the collection, analysis and interpretation of the data. Its importance can be seen in day to day life where even a layman uses statistics without even studying it, for example- a farmer deciding the price of its crop keeping in mind the land he used and crop harvested then the middlemen selecting a sample of the crop and estimating the quality of whole crop on the basis of the sample.

Statistics helps in calculating the per capita income, inflation rate, unemployment rate etc. on which basis different countries compare each other, its statistics that help to derive the information from the data and calculate all the measures which are required to check the health of the economy. For example- India is the fastest growing economy in the world because its GDP growth rate is more than 7%, which is calculated through statistics.

Another sector which can help us in realizing the importance of statistics is the banking sector, banks take deposit from the people who have excess of money and lend money to the people who need it for investment or any other purpose. Now, banks use statistical approaches such as probability to calculate the depositors who withdraw money on a certain day these approaches help banks to make profit because banks make profit out of these deposits by lending other on a higher interest rate than paid to depositors.

Few topics covered under statistics-

The topics that a student encountered first in statistics are measures of central tendency which are also known as mean, mode and median. These are the most commonly used measures in all the branches of mathematics, therefore a student need to have strong understanding of these measures. Below is a slight inside to these measures-

Mean- it's an average of the numbers which can be simply calculated by summing up all the numbers divided by the how many numbers there are. For example the mean of numbers 5,4,6,7,8 will be 7.5(5+4+6+7+8/4=7.5).

Mode- it's the highest occurring number in the data or the number appeared most in the data and most likely to get sampled. For example- the mode of the numbers 5,4,9,6,9,9,7,9,8,9 is 9.

Median- it's the number that divides the data in two equal parts, one part where all the values will be less than the median and the other part where all the values will be larger than median. For example- the median of the numbers 2,3,5,4,1,6,7,9,8 is 5( arranging the numbers in ascending order 1,2,3,4,5,6,7,8,9 gives median =5)

The empirical formula which tells the relation between mean, mode and median is-

3median = mode + 2mean

Another most studied topic of statistics is probability; it tells us the likelihood or the chances that an event will occur. For example on tossing an unbiased coin probability tells us that there is an equal probable chance of coming a head or a tail. Mathematically probability can be calculate as number of favorable outcomes divided by the number of total outcomes, it is important to note that the value of the probability of an event will lie between 0 and 1. When the value of the probability is 0 it means there is no chance that the event will occur on the other hand the probability value 1 mean it's a sure event.

Difficulties faced by student while solving genetic problems

Genetic problem is the study of the phenotype (the set of observable characteristic of an individual) of parents and their offspring to understand how the genes affect traits. The most difficult part for the student in solving the genetic problem is having a lack of understanding of genetics, fertility; chromosomes, traits etc. therefore having a better knowledge of genetics can give more clarity to students and reason behind solving these problems. Another problem faced by the student is about the hypothesis testing where the students have to make judgment and decisions about the genotypes of the parents and then the decision to accept or reject the hypothesis. These problems can create type I (rejecting the null hypothesis when it's true) and type II (accepting the null hypothesis when it's false) errors.

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