Question

Exercise 13. Suppose I tell you that the following list of 20 numbers is a random sample from a Gaussian random variable, but I don't tell you the mean or standard deviation. Also, around one or two of the numbers was corrupted by noise, computational error, tabulation error, etc., so that it is totally unrelated to the actual Gaussian random variable. -1.2045, -1.4829, -0.3616, -0.3743, -2.7298, -1.0601, -1.3298, 0.2554, 6.1865, 1.2185 一2.7273.-0.8453.-3.4282.-3.2270.-1.0137, 2.0653.-5.5393,-0.2572.-1.4512. 1.2347 To the best of your ability, determinc what the mean and standard deviation are of this random variable. Supposing you had instead a billion numbers, and 5 or 10 percent of them were corrupted samples, can you come up with some automatic way of throwing out the corrupted samples? (Once again, there could be more than one right answer here; the question is intentionally open-ended.)

Answer 1

Using Z score we do not find any outlier (since no observation lies outside the interval (-3,3)).

From box plot we observe that there is one outlier i.e. 6.1865 and it is a corrupted sample.

So mean excluding 6.1865=-1.17149

and standard deviation excluding 6.1865=1.82165307