Basics of Probability and Statistics Week 1 Challenge

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

Variance is how far a set of numbers are spread out

To put it simply (n−1) is a smaller number than (n).
When you divide by a smaller number you get a larger number.
Therefore when you divide by (n−1) the sample variance will work out to be a larger number.

2. Difference between stratified and clustered sampling

* Stratified Random Sampling
Stratified random sampling starts off by dividing a population into groups with similar attributes.
Then a random sample is taken from each group. This method is used to ensure that different
segments of a population are equally represented. The groups for stratified sampling are homogeneous.
* Cluster Random Sampling
Cluster sampling starts by dividing a population into groups
What makes this different that stratified sampling is that each cluster must be representative of the population.
Then randomly select entire clusters to sample. the clusters created in group sampling are heterogeneous

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

* The simple random sampling with replacement, the total number of possible samples is N^n.

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

No.of card = 52
Jack = 4 --> 4c2 --> 4*3/2*1 --> 6

Favorable events/ Total possible events --> 6/52 --> 3/26

Answer = 3/26

or

jack = 4/52 = 1/13

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

Total possible events = 36

Favorable events = (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)

Answer = 6/36 --> 1/36

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

Standard deviation (SD) is the most commonly used measure of dispersion. It is a measure of the spread of data about the mean. SD is the square root of
the sum of squared deviation from the mean divided by the number of observations. Standard deviation measures how data is dispersed relative to its
mean and is calculated as the square root of its variance. The further the data points are the higher the deviation. Closer data points mean a lower deviation.