Basics of Probability and Statistics Week 1 Challenge

Week 1 Challenge

Q1. Why there is a difference in the formula of variance for population and sample?

Ans:-

The formula of variance for population is σ2 = ∑(x_i - u)/N. And formula of variance for sample is s2 = ∑(x_i - u)/N-1

For population, We are consider for whole data N. N is represent all the events/numbers that present in that data.

For sample, We are consider only one small group of the data. So that group will represent N-1.

Q2. Difference between stratified and clustered sampling.

Ans:-

Stratified sampling

Clustered sampling

1. In Stratifies Sampling the population is divided into smaller sub group called strata. 2. The Division is take place based characteristics that they share 3. Each stratum is then sampled using another probability sampling method, such as simple random sampling, 4. Stratified sampling is the best choice among the probability sampling methods when you believe that subgroups will have different mean values for the variable. 5. Group are created in stratified sampling are homogenous.

1. In Cluster sampling refers to a sampling method wherein the members of the population are selected at random, from naturally occurring groups called 'cluster'. 2. In Cluster Sampling, the aim is to reduce cost and increase the efficiency of sampling. 3. All the individuals are taken from randomly selected clusters. 4. Cluster sampling is a method of probabilty sampling that is often used to study large populations, particularly those that are widely geographically dispersed. 5. Groupp are created in clustered sampling are Hetrogenous.

Q3. How many different samples can be created out of population of size n

Ans:- Based on Probability we can create sample by using following 4 methods.

1.Simple Random Sampling.

2.Systematic Sampling.

3. Stratified Sampling

4. Clustered sampling

Based on Non-Probability Mecthod we can create sample by using following Methods.

1. Convenience Sampling.

2. Quota Sampling

3. Judgement Sampling

4.Snowball Sampling.

Q4. What is the probability of drawing 2 jacks from a pack of card

Ans:- Lets say the card of 52 has 4 jack, the if we want to find out the probability of drawing 2 jack, we say p = 2/52.

that means the probability of getting 2 jack is 1/26.

Q5. What is the probability that both the numbers on dice are same while rolling 2 dice

Ans:- lets we rolle the dice

s = { (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)}

The probability of both outcomes is equal is 1/6.

Q6. Why standard deviation when variance can measure the dispersion in data

Ans:- In the variance we squere the difference of mean and x point beacuse as we did not squere it,the value will come as negetive and we get zero variance. But when we square the differnce the value is increse,so to decrese the value we use standerd deviation.

Standerd deviation is nothing but squre root of variance.