Basics of Probability and Statistics Week 1 Challenge

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

A. The formula for variance for the population is:

`sigma`^2 =`Sigma`(`X i`- `mu`)^2 /N

The formula for variance for the sample is:

`sigma`^2 =`Sigma`(`X i`- `mu`)^2 /(N-1)

The difference between the formulae is (n-1) in the denominator for the second formula.

It is because By decreasing the denominator gives the result higher and also more accurate.

2. Difference between stratified and clustered sampling?

These kinds of samplings are mostly used when the project is dealing with population data.

stratified sampling	clustered sampling
Here in this sampling population is divided into a few subgroups. There will be homogeneity within the subgroups. And heterogeneity between subgroups. Choice of elements from within each subgroup. Mostly adopted by many organizations.	Whereas here in clustered sampling, the population is divided into many subgroups. Here heterogeneity within subgroups. Homogeneity between subgroups. Random choice of subgroups. Less usage in organizations.

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

A. Let us consider the size of the population as 3.

X= {1,2,3}

The possible outcomes are -{1}{2}{3}{1,2}{1,3}{2,3}{1,2,3}, which are 7 outcomes.

When it compares to actual formula= `2^n-1`= 8-1= 7.

Which is the same as the number of outcomes in the data set.

So, The different samples that can be created out of a population of size n are = `2^n-1`.

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

A. We know that a pack of cards contains 52.

When 2 cards are drawn from a pack of cards, then the probability is= `52_(C_2)`= (52*51)/2=1326.

We also know that pick there are 4 jacks in a pack of cards.

Then picking 2 cards from 4 jacks, the probability will be =`4_(C_2)`= (4*3)/2=6.

The actual formula for probability is= the number of favourable outcomes / total number of outcomes= 6/1326=1/221.

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

A. When 2 dices are rolled, the total number of outcomes will be = (6*6)=36.

The set of favourable outcomes are= {1,1}{2,2}{3,3}{4,4}{5,5}{6,6}

No.of favourable outcomes are = 6.

Probability = (6/36)=1/6.

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

The reason for use of standard deviation is because when the variance has been calculated. The units will be in Squares, which is not possible.

For example: Variance= 10 Km^2/hr^2.

When the standard deviation is applied, then the squares will get removed (Km/hr).