Basics of Probability and Statistics Week 1 Challenge

1. Population Variance :σ² = Σ (x_i – μ)² / N

Sample Variance : s² = Σ (x_i – x)² / (n-1)

The difference between these two is when we calculate Population variance we divide by N in sample Variance by n-1.

2. In Cluster Sampling, the sampling is done on a population of clusters therefore, cluster/group is considered a sampling unit.

In Stratified Sampling, elements within each stratum are sampled.

In Cluster Sampling, only selected clusters are sampled.

In Stratified Sampling, from each stratum, a random sample is selected.

In Cluster Sampling, the aim is to reduce cost and increase sampling efficiency.

In Stratified Sampling, the motive is to increase precision to reduce error.

3. There will be 4 Jack in a deck of 52 cards the probability of getting 2 Jack is 12/2652=0.00452

4. 1/6

The number of possible outcomes is 36 if getting the same number on both dice is taken as an event in the first event number of outcomes is 6 and the second number of outcomes/ total number of possible outcomes

5. the mean is the average of the range of given data values, a variance is used to measure how far the data values are dispersed from the mean, and the standard deviation is used to calculate the amount of dispersion of the given data set values.