Consider the graphs of the two distributions given below. Determine the mean, th
ID: 3157745 • Letter: C
Question
Consider the graphs of the two distributions given below. Determine the mean, the range, and the standard deviation for each distribution. What can you say about the variability of the two distributions based on the range? Based on their standard deviations? What do you conclude from your analysis? A study of a very limited population of Aliens reveals the following number of body appendages (limbs): 2, 8. 10. 12, 18 Find the mean mu and the standard deviation sigma of this population. List all possible samples of two aliens with replacement, and find each mean. Each of the means above is called a sample mean. Find the mean of all the sample means (denoted by mu_x) and the standard deviation of all the sample means (denoted by sigma_x) for both the n = 2 samples. Verify the Central Limit Theorem: (i) compare the population mean with the mean of the sample means; (ii) compare the population standard deviations divided by the squareroot of the sample size with the standard deviation of the sample mean(i.e. sigma_x = sigma/squreroot n)Explanation / Answer
Write the data points based on the distributions. For eg. the 1st dist. is a set of points:1,2,3,3,3,3,3,3,4,5
Average = sum of obs. /number of obs. The mean is 3 for both distributions
Stddev = sqr root (submissions of squares of each point from mean of obs. divided by number of number of obs.). It is 1.05 for 1st distribution and1.94 for the second distribution. Please google the formulae, as they are ubiquitous.
Comment: Although the means are the same for both dist. (3 in our case), the Standard devaitions are different. Since number of points for both dist. are same( 10) we can comment based on standard devaitions that variability of 1st distribution is almost double( 1.05 vs. 1.94). That means data points of 2nd distribution is more spread out from the mean. A test taker' mind set is to test how same mean but diff. variability would effect the distributions.
One can comment by just oberserving the 2nd graph that heavier data points are not centered around the mean as they are in the 1st distribution. Therefore, it has more variability. The 1st graph data points are more 'centered' around the mean and therefore have less standard deviation or 'variablity'