Basics of Probability and Statistics Week 1 Challenge
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Why there is a difference in the formula of variance for population and sample
ANS:
The variance is a way to measure the spread of values in a dataset.
The formula to calculate population variance is:
σ2 = Σ (xi – μ)2 / N
where:
Σ: A symbol that means “sum”
μ: Population mean
xi: The ith element from the population
N: Population size
The formula to calculate sample variance is:
s2 = Σ (xi – x)2 / (n-1)
where:
x: Sample mean
xi: The ith element from the sample
n: Sample size
When we calculate population variance, we divide by N (the population size).
When we calculate sample variance, we divide by n-1 (the sample size – 1)
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Difference between stratified and clustered sampling
ANS:
Stratified and cluster sampling may look similar, but bear in mind that groups created in cluster sampling are heterogeneous, so the individual characteristics in the cluster vary. In contrast, groups created in stratified sampling are homogeneous, as units share characteristics.
Relatedly, in cluster sampling you randomly select entire groups and include all units of each group in your sample. However, in stratified sampling, you select some units of all groups and include them in your sample. In this way, both methods can ensure that your sample is representative of the target population.
stratified sampling
1) Stratified sampling is one, in which the population is divided into homogeneous segments, and then the sample is randomly taken from the segments.
2) Randomly selected individuals are taken from all the strata.
3) To increase precision and representation.
clustered sampling
1) Cluster sampling refers to a sampling method wherein the members of the population are selected at random, from naturally occurring groups called 'cluster'.
2) All the individuals are taken from randomly selected clusters.
3) To reduce cost and improve efficiency.
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How many different samples can be created out of population of size n
ANS:
The size of the sample to be taken is equal to the size of the population. This means that the number of different random samples that can be taken is 1 . This is because when the first sample is taken, it includes all the items in the population and so will any other sample that is taken after that. Thus all samples will have the same items
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What is the probability of drawing 2 jacks from a pack of card
ANS:
a pack contain 52 cards
jacks are 4 cards
but drawing 2 jacks from a pack of card
the probability of drawing 2 jacks from a pack of card = 2/52 = 1/26
The probability is 2/52.
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What is the probability that both the numbers on dice are same while rolling 2 dice
ANS:
each die contain 6 numbers
two dies contain 36 outcomes
two dies contains similar numbers [{1,1},{2,2},{3,3},{4,4},{5,5},{6,6}] in two dies 6
the probability that both the numbers on dice are same while rolling 2 dice = 6/36 = 1/6
∴ The probability of getting the same number of both the dice is 1/6.
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Why standard deviation when variance can measure the dispersion in data
ANS:
In short, the mean is the average of the range of given data values,
a variance is used to measure how far the data values are dispersed from the mean,
and the standard deviation is the used to calculate the amount of dispersion of the given data set values.
The standard deviation,
as the square root of the variance gives a value that is in the same units as the original values,
which makes it much easier to work with and easier to interpret in conjunction with the concept of the normal curve