Question

Find the standard deviation for a set of data that has a mean of 100 and 95% of the data falls between 70 and 130.

** Please show me the procedure, thanks!!!

Answer 1

We are given,

range = 70 to 130

By 66-95-99.7 rule, it says that:

66% of the data falls under 1 standard deviation

95% of the data falls under 2 standard deviations and

99.7% of the data falls under 3 standard deviations.

For a certain range which is 70 to 130 we will use for 95% of the data :

where n shows the number of standard deviations.

Answer.

Similarly, we can also, obtain standard deviation from the upper limit too:

Answer.

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For self-verification, we can also do this, if the obtained standard deviation is correct:

for 2 standard deviations means mean will deviate with 2*(SD) which is 2*(15) = 30

which is also, which is nothing but the means from which 30 units i.e. 2(SD) will deviate.

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