Basics of Probability and Statistics Week 1 Challenge

1. Why there is a difference in the formula of variance for population and sample?

Ans. Compare formulas of variance of population and variance of a sample.

Variance of population is `σ 2 = ∑ ( x i − μ )^2/ N`

Variance of sample is `s 2 = ∑ ( x i − μ )^2/ (N-1)`

From formulas, we can say that the variance of the population is greater than the variance of sample.

The main difference can be found in the denominator as (N-1) is smaller than the N which leads to a greater value of the variance of a population.

2. Difference between stratified and clustered sampling?

Ans. Stratified sampling: This type of sampling contains strata or groups based on the data of population by differentiating in characteristics such as age, gender, group etc., This sampling helps to represent the data by segregating them based on colour and find statistics.

Clustered sampling: A similar strategy to grouping the population into clusters based on a different trait is used in this method. Cluster sampling, on the other hand, is employed when the population is huge and it is difficult to build clusters that reflect all data points. In this scenario, the sample is drawn from only a few clusters rather than all of them. As a result, clusters are misrepresented or biasedly represented in the samples generated.

3. How many different samples can be created out of population of size n?

Ans. By considering population of size 3 as X = {A,B,C}

The possible samples are {A}, {B), {C}, {A.B} {A.C} {B.C}, {A,B, C}.

Total samples = 2^3 -1 = 7

Therefore, the total number of samples that can be generated from a population of
size N = `2^N - 1`

4. What is the probability of drawing 2 jacks from a pack of card?

Ans: No of jacks are 4...

The probability of getting two jacks is P = 4C2/52C2 = 1/221

5. What is the probability that both the numbers on dice are same while rolling 2 dice?

Ans: Outcomes are = ((1,1), (2,2), (3,3), (4,4), (5,5),
(6,6)}
no of favorable outcomes = 6
Total number of outcomes = 36
Probability that both the numbers on dice are same while rolling 2 dice is P = 6/36 = 1/6.

6. Why standard deviation when variance can measure the dispersion in data?

Squaring the difference between the variable and its mean yields the variance of a data set. As a result, the unit of variance is not dimensionally equivalent to the unit of mean.
Standard deviation, which is the square root of variance, is used to solve this problem. Both the mean and the standard deviation have the same dimension.