Basics of Probability and Statistics Week 1 Challenge

1)The difference in the formula of variance for population and sample . Because variance is calculated generally as sum[(obs – mean)^2]/(number of obs.) but sometimes sample mean comes out to be very different than population mean and hence denominator of the given equation is small for sample and hence it underestimate the sample variance. To correct it we use the n-1 instead of n.

2)> Cluster sampling is a type of sampling method in which we split a population into clusters, then randomly select some of the clusters and include all members from those clusters in the sample.

> Stratified sampling is a type of sampling method in which we split a population into groups, then randomly select some members from each group to be in the sample.

similarities in both sampling techniques

• Both methods are examples of probability sampling methods – every member in the population has an equal probability of being selected to be in the sample.
• Both methods divide a population into distinct groups (either clusters or stratums).
• Both methods tend to be quicker and more cost-effective ways of obtaining a sample from a population compared to a simple random sample.

differences in both sampling techniques

• 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.

>If a population is homogeneous (i.e. there are no noticeable differences between individuals) then it’s best to use cluster sampling to obtain a sample.

>If a population is heterogeneous (i.e. there are natural differences between individuals) then it’s best to use stratified sampling to obtain a random sample.

3)We're gonna do another accommodation problem that us is how many different samples of size and could be selected from within a population. Oh, size, large. And so, in this case, if we were to write our, um, our notation, it would be big and see little end. And in this case, big end will always be the same. Off number 1000. However, little end is what's changing each part. So in part A, it tells us that little and is five, so we can go ahead and write 1000 C five and, um, in part B. I'm just gonna go ahead and write out all the negotiations and then we can go through insult them. So for part B, it would be 1000 seek 15 and then for Parsi, it would be 1000 C 30. Okay, so now we have the notations for all three parts. If you're not sure how to do this on your calculator, I'm gonna go through and explain that once. So you click on mask the button that says map and then you go to prom. I don't look like this and then uses were doing combinations. You'll go to Button three, which should say and see are OK, this is for a T I 84 calculator. Okay, Um and then once you had on NCR, you'll get, like, a like A You'll go back to the home page and it would be kind of like this With were these two are like blanks and you control them. And so, for example, for part, For the first part, we would want to put 1000 here and five here. So we're gonna go through and just enter that into our calculator. Oh, 1000 C five gives us it's 0.25 times 10 to the 12th. Ah, 1000 C 15 gives us 6.8 age times 10 to the 30 seconds on day one dozen see 30 gives us 2.43 times 10 to 57. Okay, I hope that was helpful. And I hope you have a great day

4)since there are a total of 4 jacks in a deck of 52, the probability of the getting the first jack is 4:52 = 4/52 = 1/13
.
Now, after the first jack is removed, there are only 3 jacks left in a deck of 51 so the probability of the second card drawn is:
3:51 = 3/51 = 1/17

Therefore the probability is:
1/13 * 1/17 = 0.0045

5)

Sample points of getting same number on both dice- (1,1) ,(2,2) ,(3,3) ,(4,4) ,(5,5) & (6,6).

Thus, 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.

6)The average squared deviation from the mean of the given data set is known as the variance. This measure of dispersion checks the spread of the data about the mean. Standard Deviation: The square root of the variance gives the standard deviation. Thus, the standard deviation also measures the variation of the data about the mean.