Basics of Probability and Statistics Week 1 Challenge
1. Why there is a difference in the formula of variance for population and sample?
We divide by N (the population size), When we calculate sample variance, we divide by n-1 (the sample size – 1).
2. Difference between stratified and clustered sampling
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
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.
3. How many different samples can be created out of population of size n
Lets assume Population Size = N
and sample size = n
so the total number of samples created is = NCn
4 . What is the probability of drawing 2 jacks from a pack of card
Total number of cards are 52 and number of red cards are 26 and jacks are 4 whereas 26 red cards contain 2 Jacks (so only 2 will be considered out of 4). So, total outcomes = 52 favorable outcomes = 26 + 2 = 28 So, the probability of getting a jack or red card = Favorable outcomes / Total outcomes = 28 / 52 = 7/13
5. What is the probability that both the numbers on dice are same while rolling 2 dice
[ (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) ]
So, pairs with same numbers are (1,1) (2,2) (3,3) (4,4) (5,5) (6,6) i.e. total 6 pairs
Total outcomes = 36
Favorable outcomes = 6
Probability of getting pair with same numbers = Favorable outcomes / Total outcomes = 6 / 36 = 1/6
So, P(N, N) = 1/6.
6. Why standard deviation when variance can measure the dispersion in data?
Square root of varience is equal to Standard Deviation.
sigma = Std.Dev
sigma**2 = Varience
Variance is a method to find or obtain the measure between the variables that how are they different from one another, whereas standard deviation shows us how the data set or the variables differ from the mean or the average value from the data set.