Basics of Probability and Statistics Week 1 Challenge
Q1. Why there is a difference in the formula of variance for population and sample
- This has to do with a concept called Degrees of freedom (statistics). It basically means the number of variables that are free to vary.
- Because , The first (n-1) samples are independent of each other given the mean, but the last one is not , you can find the last value , given the n-1 values and the mean.
- degrees of freedom is becomes n - 1 instead of n. It is a slightly convoluted concept but basically the since we are estimating a population mean using a sample, this is one way reduce the bias and make the sample variance somewhat unbiased estimator of population variance.
Q2. Difference between stratified and clustered sampling
- 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.
Q3. How many different samples can be created out of population of size n
- 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.
Q4. What is the probability of drawing 2 jacks from a pack of card
Answer : `1/221`
Q5. What is the probability that both the numbers on dice are same while rolling 2 dice
Answer : `1/6`
Q6. Why standard deviation when variance can measure the dispersion in data
- 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.
- We know that the measures of dispersion can be categorised into two different types, namely absolute measure of dispersion and the relative measure of dispersion. When we consider the variance and standard deviation, both fall under the absolute measure of dispersion. Before discussing the key difference between the variance and the standard deviation let’s discuss the definition of variance and the standard deviation here.