Basics of Probability and Statistics Week 1 Challenge

Q1.

The value of variance and standard deviation, which is squared root of variance are higher in case of sample data than variance from population data.Due to this value of denominator in the formula for variance in case of sample data is 'n-1', and it is 'n' for population data.

Q2.

• In Cluster Sampling, the aim is to reduce cost and increase the efficiency of sampling.
• In Cluster Sampling, the sampling is done on a population of clusters therefore, cluster/group is considered a sampling unit.
• In Cluster Sampling, only selected clusters are sampled.
• In Stratified Sampling, elements within each stratum are sampled.
• In Stratified Sampling, from each stratum, a random sample is selected.
• In Stratified Sampling, the motive is to increase precision to reduce error.

Q4.

There are 52 cards in a deck of cards. 

Hence, total number of outcomes = 52

The number of favorable outcomes = 2 (but there are 4 jacks in a deck)

The probability of drawing a jack in the 1st draw = 4/52

The probability of drawing a jack in the 2nd draw= 3/51

(4/52) * (3/51)=0.00452

Q5.

Number of outcomes while rolling two dice = 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).

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.

Q6.

Standard deviation measures how far apart numbers are in a data set.
Variance, on the other hand, gives an actual value to how much the numbers in a data set vary from the mean.
Standard deviation is the square root of the variance and is expressed in the same units as the data set.

Note:

I have attached text file for answers for reference