Basics of Probability and Statistics Week 1 Challenge
Q1)Why there is a difference in the formula of variance for population and sample
ANS:
There is a difference in the fromula of a variance for the population and sample that why Because variance is calculated generally as sum[(obs – mean)^2]/(number of obs.) for the population, but sometimes sample mean comes out to be very different than population mean and hence denominator of the given equation is small for sample and hence it underestimate the sample variance. To correct it we use the n-1 instead of n.
Q2)Difference between stratified and clustered sampling
ANS:
Cluster sampling is a type of sampling method in which we split a population into clusters, then randomly select some of the clusters and include all members from those clusters in the sample.
example for the cluster sampling is the for a school students in a classes list out the names for a exibtion then in a school students classes are the cluster sampling
Stratified sampling is a type of sampling method in which we split a population into groups, then randomly select some members from each group to be in the sample.
example for the Stratified saampling is a for the population of a country male and female as a stratified sampling.
Q3)How many different samples can be created out of population of size n
ANS:The different samples can be created out of population of size n by using the formula of Ncr let us take a one example for better understanding of different samples can be created out of population of size n
The population size is N=12. The number of possible samples of size n=3 Then by applying above Ncr
12!/3!*(12-3)! by calculating we get the The number of samples 220
Q4)What is the probability of drawing 2 jacks from a pack of card
ANS:In a pack of card total 52 cards in that there are 4 jacks from total cards so probabilty for 4 cards is 4/52
the probability for 3 cards is 3/51 so the probability of drawing 2 jacks from a pack of card ia 4/54 * 3/51 is 0.0045
Q5)What is the probability that both the numbers on dice are same while rolling 2 dice
ANS:
the probability of an event is Favorable outcomes/Total number of outcomes
when a one dice rolls it has a 6 outcomes when two dice are rolling then the total no of outcomes are 36
and he probability that both the numbers on dice are same while rolling 2 dice are the favourable outcomes are 6 then 6/36
probability that both the numbers on dice are same while rolling 2 dice is 1/6
Q6)Why standard deviation when variance can measure the dispersion in data
ANS:
Standard Deviation is a measure of how much the data is dispersed from its mean.A high standard deviation implies that the data values are more spread out from the mean.
Variance is the square of the standard deviation. Being a squared term, it is non-negative. The unit of variance is squared unit, thereby making it less intuitive. Moreover, standard deviation is preferred over variance because standard deviation can be compared with the mean