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

As a result, the calculated sample variance (and therefore also the standard deviation) will be slightly higher than if we would have used the population variance formula. The purpose of this little difference it to get a better and unbiased estimate of the population‘s variance.

2.Difference between stratified and clustered sampling

Startified Sampling: Stratified sampling is one in which the population is divided into homogeneous segments, and then the sample is randomly taken from the segments.

Here the population are chosen randomly from the segments.

Cluster Sampling:Cluster sampling refers to a sampling method wherein the members of the population are selected at random, from naturally occurring groups called 'cluster'.

Here the population is selected from the cluster.

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

There are 52 cards in a pack and drawing 2 jacks from this pack of cards gives the probability 2 out of 52 i.e. 2/52 which reduces to 1/26

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. 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 Variance is calculated as shown above, and then take the square root of it we can get the standard deviation.Taking the square root of the variance gives us the units used in the original scale.Standard deviation is a statistic that shows how far from the mean a group of numbers is, by using the square root of the varience.