Basics of Probability and Statistics Week 1 Challenge
1.Why there is a difference in the formula of variance for population and sample?
ans: Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data. Due to this value of the denominator in the formula for variance in the case of sample data is 'n-1' , and it is in 'n' for population data.
2.Difference between stratified and clustered sampling?
ans: BASIS FOR COMPARISION STRATIFIED SAMPLING AND CLUSTER SAMPLING
Meaning Stratified sampling is one, in which the population is divided into homogeneous segments, and then the sample is randomly taken from the segments.Cluster sampling refers to a sampling method where in the members of the population are selected at random, from naturally occuring groups called 'cluster'.
Sample Randomly selected individuals are taken from all the strata. All the individuals are taken from the randomly selected clusters.
Selection of population elements individually Collectively
Homogeneity Within group between groups
Hetrogeneity Between groups within group
Bifurcation imposed by the researcher Naturally occuring groups
Objective to increase precision and representation. To reduce cost and improve efficiency.
3.How many different samples can be created out of population of size n?
ans: For N size of population the n different samples can be created if there is no replacement.
=n!
4. What is the probability of drawing 2 jacks from a pack of card?
ans: The probability of drawing 2 jacks from a pack of cards is : 2/52
(i.e,)1/26
5.What is the probability that both the numbers on dice are same while rolling 2 dice?
ans: Since,the number of outcomes while rolling a dice = 6
Number of Outcomes while rolling two dice = 62
=36
The Sample Space for rolling a die is given as,
{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
Sample points of getting same number on both dice - (1,1),(2,2),(3,3),(4,4),(5,5) & (6,6).
Thus, the number of favourable outcomes = 6
Total number of outcomes = 36
P (getting same number on both dice) = 6/36
= 1/6
Hence, the probability of getting same number on both the dice is 1/6.
6.Why standard deviation when variance can measure the dispersion in data
ans: Standard Deviation is best in measuring the dispersion in data then variance because
It is based on all values and thus,provides information about the complete series because of this ,a change in even one value affects the standard deviation value.
It is independent of origin not of scale.
It is helpful in advanced statistical calculations like the comparision of variability in two data sets.
It can be used in the testing hypothesis .
It is Capable of further algebraic treatment