Basics of Probability and Statistics Week 1 Challenge

1.

• Why there is a difference in the formula of variance for population and sample

Formula of variance for population =∑(Xi−u)2/n
Formula of variance for sample =∑(Xi−u)2/n-1

Because variance for population is calculated from the population data,and the variance for sample is calculated from sample data which we have chosen from the
population data. So sample data is not the whole population data. Therefore there is a difference in variance for population and sample.
for ex :- population = 2,4,6,8,10
mean for population = 6
variance = 40/5
variance for population = 8
sample = 2,4,6
mean = 4
variance = 8/2
varaince = 4

2.

• Difference between stratified and clustered sampling

Stratified sampling :- In stratified sampling the strata/groups can be heterogeneous and the elements in the strata/groups can also be heterogenous.
Clustered sampling :- In clutered sampling the cluster/groups can be heterogeneous but the elements in the cluster/groups must be homogeneous.

for ex :- There are 10 boys and 5 girls
Stratified = { 3 boys 2 girls} , {3 girls 2 boys} , {5 boys}
Clustered = {5 boys} , {5 boys} , {5 girls}

3.

• How many different samples can be created out of population of size n

n number of different samples can be created out of population of size n

4.

• What is the probability of drawing 2 jacks from a pack of card

Probability of drawing 2 jacks from a pack of card
prob = favourable event / total outcomes
prob = 2/52
prob = 1/26

5.

• What is the probability that both the numbers on dice are same while rolling 2 dice

probability of both the numbers on dice are same while rolling 2 dice
prob = favourable event / total outcomes
prob = 6/36
prob = 1/6

6.

• Why standard deviation when variance can measure the dispersion in data

Standard Deviation is used to get back the original unit of observations
for ex :- if the unit for observations is km/h
mean will be km/h
but the variance will be km2/h2

so to get back the original unit of observations we apply standard deviation