Suppose we have some raw data. We randomly select two observations from this dat

Question

Suppose we have some raw data. We randomly select two observations from this dataset, then record the mean of those two observations. We do this over and over again, and in so doing we create a new dataset, consisting of the means of samples of size n- 2 from the original data. Next, we perform the same procedure of randomly selecting observations from the original dataset and taking the mean, except this time we take samples of size n=4, and record these as another new dataset. Finally, we perform the same procedure again with samples of size n=100. Below are four histograms, labeled A, B, C, and D. Identify which is the histogram of raw data, and which are the histograms of the sample means for n=2, n-4, and n=100. (You have four tries for this problem, and you must all identify four histograms correctly for credit; select answers for all four before submitting.) raw data. n 2 n-100

Explanation / Answer

Histogram of raw data: D

Histogram of the sample means for n = 2 : B

Histogram of the sample means for n = 4 : C

Histogram of the sample means for n = 100: A

EXPLANATION: Raw data will be having outliers and with wide variability. This is reflected in Histogram D. The distribution of sample means approaches Normal Distribution as n incerases from n= 2, then n=4 and finally n= 100 as depicted in Histograms B,C and A respectively.

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