Bias in Mathematical Terms

Introduction to bias in mathematical terms:

Bias in mathematical terms is applicable to the die or dies problem, biased dies are not give the probability of the equal number such as (2,2), example in standard die the number 3 will be appear in 6 chances (it means we have to roll the die 6 times )so the probability is 1/6.but in the biased die the number 3 will be appear 3 times in 6 rolls so the probability is 3/6=1/2


Types of bias- bias in mathematical terms:


In statistics the bias can be classified as many types

Selection bias
Systematic bias
Data-snooping bias
Statistical hypothesis testing
Sampling bias
Inductive bias
Notation bias
Publication bias
Infrastructure bias
Cognitive bias
Cognitive bias- bias in mathematical terms:

In this type only one bias we called as the conformation bias. I have recently faced lot of problem while learning Definition of Rational Number, But thank to online resources of math which helped me to learn myself easily on net.


Example problems - bias in mathematical terms:


Biased estimation is used to estimate the standard deviation of population it will be calculated by using the standard deviation of sample of size m

Solution:

Consider m=1

Here m is the standard deviation of sample size, so the standard deviation of sample size 1 will be always zero, so we cannot find the deviation for the single value, so we can tell the estimation is zero and the average of the standard deviation is zero, but in generally the population have some standard deviation value, so the above estimation will be the biased

Example 2:

Find the value of 13.39`xx` 3.45?

A) 461955

b) 461.955

c) 46.1955

D) 4619.55

Solution:

In the problem after decimal 2 digits are there (for both), therefore the product must contains 4 decimal places

1339`xx` 345=461955(here we did not consider decimal we consider only the digit)

Now take the decimal

46.1955

So the answer is c

(So here the biased question are based on the assumptions)