![]() Here Σ i k i means the sum of the k i outcomes. Then the formula for the mean if there are N draws is μ = Σ i k i/ N. For example, from the table, k 1 = 1 and k 5 = 0. Whether or not that guess holds can be checked by looking at Table 16.9 and calculating the mean of the outcome. Before you read any further, ask, “What do you think the average ought to be from the coin flipping exercise?” It is natural to say 0.5, since half the time the outcome will be a head and thus have a value of zero, whereas the remainder of the time the outcome will be a tail and thus have a value of one. The first is the mean (or average) and is a measure of central tendency. We use the data from the table to define and illustrate two statistics that are commonly used in economics discussions. Both the pie chart and the bar diagram are commonly found in spreadsheet programs.Įconomists and statisticians often want to describe data in terms of numbers rather than figures. Alternatively, a pie chart is often used to display this fraction. One possibility is a bar graph in which the fraction of observations of each outcome is easily shown. Even before you start to compute some complicated statistics, having a way to present the data is important. ![]() There are many ways to summarize the information contained in a sample of data. Whether a coin comes up heads or tails on any particular flip does not depend on other outcomes. Keep in mind that the realization of the random number in draw i is independent of the realizations of the random numbers in both past and future draws. ![]() The choice of 0.5 as the cutoff for heads reflects the fact that we are considering the flips of a fair coin in which each side has the same probability: 0.5. To generate this last column, we adopted a rule: if the random number was less than 0.5, we termed this a “tail” and assigned a 0 to the draw otherwise we termed it a “head” and assigned a 1 to the draw. The third column creates the two events of heads and tails that we normally associate with a coin flip. Those choices are listed in the second column of Table 16.9. In the program we used, the function was called RAND and this generated the choice of a number between zero and one. To generate the data set, we drew 10 random numbers using the spreadsheet program. #VARIANCE OF COIN FLIP FULL#Although you might think it would be easier just to flip a coin, doing this on a spreadsheet gives you a full range of tools embedded in that program. The idea is to simulate the flipping of a two-sided coin. We can also find the standard deviation of ?X?, ?\sigma_X?, which is just the square root of the variance.To start our presentation of descriptive statistics, we construct a data set using a spreadsheet program. Let’s find the variance when ?X? is the number of heads we get when we flip a coin two times, remembering that we already found ?E(X)=1? for this probability distribution. We’ll do that for each value of ?X?, and then add all those results together to get the variance, ?\sigma_X^2?. ![]() To find the variance, we’ll take the difference between ?X? and the mean, ?\mu_X?, square that difference, and then multiply the result by the probability of ?X?, called ?P(X)?. We can also find the variance and standard deviation for discrete random variables. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |