Basics of Probability and Statistics Week 1 Challenge
Why there is a difference in formula of variance for population and sample ?
Variance is defined as the squared difference from the mean.
Variance for population is given by `σ^2=(∑▒〖(x_i-μ_x)〗^2 )/N`
Variance for sample is given by `s^2=(∑▒〖(x_i-μ_x)〗^2 )/(N-1)`
Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data.
It is expensive/not feasible to perform an analysis on an entire population; hence, most statistical methods are about drawing conclusions about a population by analyzing a sample.
Difference between stratified and cluster sampling
Stratified sampling is a type of probability sampling, in which first of all the population is bifurcated into various mutually exclusive, homogeneous subgroups (strata), after that, a subject is selected randomly from each group (stratum), which are then combined to form a single sample.
Cluster sampling is defined as a sampling technique in which the population is divided into already existing groupings (clusters), and then a sample of the cluster is selected randomly from the population.
How many different samples can be created out of population of size n ?
`2^n-1` unique samples without considering null set can be created out of population size n
For example, if we consider set of 3 numbers `{1,2,3}`then different samples can be created as follows
`{1}{2} {3}{1,2} {2,3}{1,3} {1,2,3}`
What is the probability of getting of drawing 2 jacks from a pack of card?
A pack of card contains 4 jacks
When card is drawn for the first time the probability of getting the jack is `〖4_C〗_1/52`
When card is drawn for the second time the probability of getting the jack is `〖3_C〗_1/51`
Probability of getting two jacks from pack of card `=(4/52)*(3/51)=(1/221)`
What is the probability that the numbers on both the dice are same while rolling 2 dice?
When two dice are drawn there will be 36 combinations. However possibility of getting same number would be `(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)=(6/36)=(1/6)`
Why standard deviation when variance can measure the dispersion data ?
The standard deviation is expressed in the same unit of measurement as the data. However, which is not necessarily the case with variance.