Basics of Probability and Statistics Week 1 Challenge
week 1
Q1. Population variance (σ2) tells us how data points in a specific population are spread out. It is the average of the distances from each data point in the population to the mean, squared.
σ2 is usually represented as σ2 and can be calculated using the following formula:
Sample variance is used to measure the spread of the data points in a given data set around the mean.
s2 = Σ (xi – x)2 / (n-1)
Q2.
| BASIS FOR COMPARISON | STRATIFIED SAMPLING | 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 wherein the members of the population are selected at random, from naturally occurring groups called 'cluster'. |
| Sample | Randomly selected individuals are taken from all the strata. | All the individuals are taken from randomly selected clusters. |
| Selection of population elements | Individually | Collectively |
| Homogeneity | Within group | Between groups |
| Heterogeneity | Between groups | Within group |
| Bifurcation | Imposed by the researcher | Naturally occurring groups |
| Objective | To increase precision and representation. |
To reduce cost and improve efficiency. |
Q3.There are four primary, random (probability) sampling methods – simple random sampling, systematic sampling, stratified sampling, and cluster sampling.
N usually refers to a population size, while n refers to a sample size. Can also consider n to be the within-cell size, while N is the entire-sample size.
Q4. 2jacks of deak 2/52 (or) 0.038
Q5.When two dice are rolled what is the probability of getting same number on both? Sample points of getting same number on both dice- (1,1) ,(2,2) ,(3,3) ,(4,4) ,(5,5) & (6,6). Hence, the probability of getting same number on both the dice is 1/6.
Q5. Standard Deviation (s) It is the better measure of dispersion compared to range and IQR because unlike range and IQR, the Standard deviation utilizes all the values in the data set in its calculation. The square of the standard deviation is called Variance(s2)