Basics of Probability and Statistics Week 1 Challenge

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

The population and sample variance is shown above and there is a small change in the denominator, the population variation has denominator 'n' which is the number of items in the population and for sample varience is one less i.e., 'n-1'.

The calculated sample varience is slightly higher than the calculated population varience. This slight difference in formula is to get better and unbiased estimate from the populationn's varience.

2.Difference between stratified and clustered sampling

Stratified Sampling: Here the population is divided in to homogeneous segments and then the sample is taken randomly from the segments.

Here the samples are taken randomly from the segments.

Cluster Sampling: Here the members of the sample are selected randomly from the naturally occured groups called 'cluster'

Here the samples are taken randomly from the naturally occured group.

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

A good maximum sample size is usually around 10% of the population, as long as this does not exceed 1000. For example, in a population of 5000, 10% would be 500. In a population of 200,000, 10% would be 20,000. This exceeds 1000, so in this case the maximum would be 1000.

Even in a population of 200,000, sampling 1000 people will normally give a fairly accurate result. Sampling more than 1000 people won’t add much to the accuracy given the extra time and money it would cost.

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

Getting two cards out of 52 is

52C2=(52x51/2x1)=1326

Getting 2 jacks out of 4 jacks is

4C2=(4x3/2x1)=6

probability of getting 2 jacks out of 52 cards is given by

P=favorable outcomes/total outcomes

=6/1326

=1/221

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

When two dice are drawn there will be 36 combinations. However, for getting the same number on both die, there will be 6 possibilities which are (1,1),(2,2),(3,3),(4,4),(5,5) and (6,6). Hence, the required probability is 6/36 which reduces to 1/36.

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

The varience is calculated as shown above (Ref:Ques No:1) and then take the sqaure root of the varience we get the standard deviation. Taking square root of varience gives us the units used in original scale also it shows how far the members are from the mean value.