Question

24,62,71,75,76,78,79,80,82,83,84,84,85,88,89,90,91,92,93,97

What is the interval contains approximately 68%,95%,99.7% of the observation?

Answer 1

For an almost normal data set,

the values within one standard deviation of the mean account for about 68% of the set and within two standard deviations account for about 95%; and within three standard deviations account for about 99.7%.

First of all we have to calculate standard deviation and mean of data.

The standard deviation of the data set is:

σ=15.6012

Mean= 80.15

Now we know that ( means.d.) contain 68% data .i.e.(80.1515.6012)

Hence interval= from 64.549 to 95.7512 , 68% data lies.

Similarly mean2*s.d. contain 95% data .

I.e. (80.152*15.6012)

hence interval= From 48.95 to 111.35

Similarly mean 3*s.d. contain 99.7% data

i.e. (80.153*15.6012)

hence interval= From 33.35 to 126.95

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