Basics of Probability and Statistics Week 1 Challenge
1. The main difference between population variance and sample variance relates to calculation of variance. Variance is calculated in five steps. First mean is calculated, then we calculate deviations from the mean, and thirdly the deviations are squared, fourthly the squared deviations are summed up and finally this sum is divided by number of items for which the variance is being calculated. Thus variance= Σ(xi-x-)/n. Where xi = ith. Number, x- = mean and n = number of items.
Now, when the variance is to be calculated from population data, n is equal to the number of items. Thus if variance in blood pressure of all the 1000 people is to be calculated from data on blood pressures of all the 1000 people, then n = 1000. However when the variance is calculated from sample data 1 is to be deducted from n before dividing the sum of the squared deviations. Thus in the above example if sample data have 100 items, the denominator would be 100 – 1 = 99.
Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data. Due to this value of denominator in the formula for variance in case of sample data is 'n-1', and it is 'n' for population data
2.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'.
Randomly selected individuals are taken from all the strata.
All the individuals are taken from randomly selected clusters.
3.
he probability of drawing two cards of the same rank consecutively is:
the chance of drawing the first card X The chance of drawing the second card.
since the first card can be any of the 4 jacks, the chances of drawing one of them is 4(jacks) / 52(cards in deck).
the second card can be any of the remaining jacks, though there are now 51 cards in the deck so the chances of the second card also being a jack are 3(jacks)/51(cards in deck)
The chances of both happening are
(4*3)/(52*51) = 12/2652 = 1/221
4.When two dice are drawn there will be 36 combinations. However, for getting the same number on both die, there will be 6 possibilities which are (1,1),(2,2),(3,3),(4,4),(5,5) and (6,6). Hence, the required probability is 6/36 = 1/6.
5.
Standard deviation measures how data is dispersed relative to its mean and is calculated as the square root of its variance. The further the data points are, the higher the deviation. Closer data points mean a lower deviation.
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).