Given the following data sets: A: 32 47 34 46 38 36 44 33 29 37 44 56 50 47 23 4

Question

Given the following data sets: A: 32 47 34 46 38 36 44 33 29 37 44 56 50 47 23 40 30 27 B: 12 43 46 30 40 30 29 34 45 47 50 45 44 48 33 36 56 39 Find the five number summary for each data set. Draw the Box Plot for the data sets. Draw the histograms for each data set. Describe the distribution for each data set Find the means and standard deviations Given that a histogram is bell shaped with mean 100 and standard deviation of 20: Where does 68 percent of the data lie? Where does 95 percent of the data lie? Where does 99.7 percent of the data lie?

Explanation / Answer

Given that the mean (u) of a normal probability distribution is 100 and the
standard deviation (sd) is 20.
(a) About 68% of the area under the normal curve is within one standard deviation of the mean. i.e.
(u ± 1s.d)
So to the given normal distribution about 68% of the observations lie in between
= (100 ± 20)
= [100-20, 100+20]
= [100-20, 100+20]
= [ 80, 120]

(b)
About 95% of the area under the normal curve is within two standard deviations of the mean. i.e.
(u ± 2*s.d)
So to the given normal distribution about 68% of the observations lie in between
=[100 ± 2 * 20]
= [ 60, 140]

(c)
Practically 99.7% of the area under the normal curve is within three standard deviations of the mean. i.e.
(u ± 3*s.d)
So to the given normal distribution practically all of the observations lie in between
[100 ± 3 * 20]
= [ 40, 160]

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