For a population, the mean is 19.4 and the standard deviation is 5.8. compare the mean and standard deviation of the following random samples to the population parameters. 25, 32, 16, 12, 11, 38, 22, 21, 19, 20

The mean of the random samples (21.6) is greater than population´s mean (19.4) and the STD of the random samples (7.96) is greater than population´s STD (5.8)

Step-by-step explanation:

To calculate the mean of the random samples, we find the average value of the data set

Where a is an element of the random example and n is the number of elements in the sample, as follows

Mean = (25+32+16+12+11+38+22+21+19+20)*(1/10) = 21.6

To calculate the STD (Standard Deviation) we need to know the variance, because

The variance is determined as the sum of the deviation from one element of the data to the mean squared, all divided by n as below.

If you calculate this by calculator or with a computer, you should get Var=63.44

And with that value, STD=7.96≈8

Therefore, by comparison, both Mean and STD of the random sample are greater than the population´s parameter

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