Basics of Probability and Statistics Week 1 Challenge
- Why there is a difference in the formula of variance for population and sample
- Population variance we mainly consider real time data and we divide the value with the total number of elements present in the data . When we consider elements like height, blood pressure of a number of people it is physically possible to compute such values but it involves a lot of time and it is computationally more expensive and we will require more time for carrying out the calculation.Hence many a times we face lack of information in the data that is present .Hence we consider all the samples present in population dataset and not sample dataset which may have a lot of information.
- Difference between stratified and clustered sampling
- 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 the efficiency of sampling.
- In Stratified Sampling, the motive is to increase precision to reduce error.
- How many different samples can be created out of population of size n
- n raised to power n
- What is the probability of drawing 2 jacks from a pack of card
- If there are 2 Jacks in a pile of 52 cards already, and you add two more Jacks, then your probablilty of drawing out a Jack is 4 out of 54 (or 4/54), and when you divide the numerator and denominator by 2/2 (because it's a factor of 1, so you don't change the equation), you get 2/26.
- What is the probability that both the numbers on dice are same while rolling 2 dice
- 1/6 ie samples (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) from the total samples.
- Why standard deviation when variance can measure the dispersion in data
- The standard deviation is usually more useful to describe the variability of the data while the variance is usually much more useful mathematically. For example, the sum of uncorrelated distributions (random variables) also has a variance that is the sum of the variances of those distributions. This wouldn't be true of the standard deviation . On the other hand, the standard deviation has the convenience of being expressed in units of the original variable.