Statistics → Variable → Average → Expected Value → Weighted Average Some points are more important than others. And, some results contribute more than others to the final result. Weighted average is an average where different quantities have different weight. And, it is calculated using the formula or Example 1. In a particular module an […]

Statistics → Variable → Average → Expected Value Expectation (Expected Value) Expected value (or expectation) is simply the average of all possible outcomes. Example 1. The price of a stock is $100. And, there are equal chances that after one year it could be $90, $110, $120 or remains the same. (a) What is the […]

Statistics → Variable → Average Average (or arithmetic mean or simply mean) is the sum of the numbers divided by total numbers. Example 1. What is the average of the numbers: 3, 8, 0, 2, 2, 0, 10 and 7? Here, total number of observations are: n = 8. Hence, Average of Percentages The average […]

Statistics → Variable A variable is a quantity whose value changes. For example, Number of students in each class/department/university Number of road accidents in a city/country Performance of university/company/government during 2018 Age or Height of students in a university Profit/Loss of a company in each year Asset/Stock prices Discrete Variable A discrete variable is one […]

Probability → Vocabulary → Formula → Example Questions → Addition of Probabilities → Multiplication of Probabilities Consider this example, a dice is rolled once, what is the probability that the number shown is Even and is four? So, this is the multiplication of probabilities. Solution to the above problem A dice is rolled, so all possible events are six {1,2,3,4,5,6}, […]

Probability → Vocabulary → Formula → Example Questions → Addition of Probabilities First consider what are joint (or not-mutually exclusive) and disjoint (or mutually exclusive) events. Suppose, we have sample space Then even and odd numbers in the above set are disjoint events. As Even Numbers = 2, 4,6 and Odd Numbers = 1, 3, 5 But, if […]

Probability → Basics → Vocabulary → Formula → Example Questions → Bernoulli Trial An experiment that has only two possible outcomes is called Bernoulli trial. For example, Pass or Fail, Dead or Alive, Head or Tail etc. For simplicity these events are called success (S) or failure (F). The probability of success is thus given by […]

Probability → Basics → Vocabulary → Formula → Example Questions → Probability as Relative Frequency In multiple choice questions, normally there are five options and the one correct answer. If a student choose an option at random, there is 1/5 probability (20% chances) of selecting the right answer. It also means that if a student do not […]

Probability → Basics → Vocabulary → Formula → Sample Space → Probability Example Questions Consider the following basic Probability Example Questions. 1. A fair dice is rolled. What is the probability of getting the number four? Solution Here, favorable events = 1 (that is 4), and total events = 6 So, , and Using probability formula […]