Basics of Probability and Statistics Week 1 Challenge
1.Why there is a difference in the formula of variance for population and sample?
-> Population variance Sample variance
1.σ2=∑(xi−μ)2/N 1. s2=∑(xi−¯x)2./(n-1)
where N is the size of the population The xi tends to be closer to
consisting of x1,x2,…xN and μμ is the their average x rather then mean,so we
population mean compensate for this by using the divisor(n-1)
rather then n.
2.Denominator is n 2.Denominator is (n-1)
3.We should calculate the 3. We should calculate the
population variance when the sample variance when the
dataset working with represents dataset working with
an entire population represents a sample taken
from large population
2.Difference between stratified and clustered sampling?
-> stratified sampling clustered sampling
1.stratified sampling is type 1.Clustered sampling is a type of
of sampling method in which we sampling method in which we split a
split a population into groups population into cluster,then randomly
then ramndomly select some select some of the clusters and include
member from each group to be all members from those clusters in the
in the sample. sample.
2.If the population is 2.If the population is homogeneous
heterogeneous use stratified then use clustred sampling.
sampling
3.Stratified sampling can be 3.Cluster sampling is very cost efficient.
expensive
4.Required a large period of time 4.Cluster sampling is time efficient.
to accomplish
3.How many different samples can be created out of population of size n?
->1.Sample size of n
2.population size N
3. NCn
example:N is population (A,B,C,D,E),n is size 2
5C2=(5*4)/(1*2)=10
{(A,B)(A,C)(A,D)(A,E),(B,C)(B,D)(B,E)(C,D)(C,E)(D,E)}
4.What is the probability of drawing 2 jacks from a pack of card?
-> (4c1/52c1)*(3c1/51c1)
(4/52)*(3/51)
=(4*3)/(52*51)
=(12)/(2652)
=1/221
5.What is the probability that both the numbers on dice are same while rolling 2 dice?
->rolling 2 dice get probability
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
1.E={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}
2.2 dice= 6*2=36
3.(total no of E)/36==6/36
6.Why standard deviation when variance can measure the dispersion in data?
->Standard deviation is the spread of a group of numbers from the mean.
The variance measures the average degree to which each point differs from the mean.
While standard deviation is the square root of the variance, variance is the average of all data points within a group.