Basics of Probability and Statistics Week 1 Challenge

1A-The only differences in the way the sample variance is calculated is that the sample mean is used, the deviations is summed up over the sample, and the sum is divided by n-1.

As data can be of two types, grouped and ungrouped, hence, there are two formulas that are available to calculate the sample variance. Furthermore, the square root of the sample variance results in the sample standard deviation.

2A-Cluster sampling divides a population into groups, then includes all members of some randomly chosen groups. Stratified sampling divides a population into groups, then includes some members of all of the groups.

3A- 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.

N usually refers to a population size, while n refers to a sample size.

4A-Required Probability =1/4×12/51=3/51=1/17 .

5A-Total number of all possible outcomes = 36.
Getting same number on both dice means getting
(1,1),(2,2),(3,3),(4,4),(5,5),(6,6).
Their number is 6.
P(getting the same number on both dice) =6/36=1/6.

6A- 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.