Question

The brain volumes

​(cm cubedcm3​)

of 20 brains have a mean of

1059.21059.2

cm cubedcm3

and a standard deviation of

128.9128.9

cm cubedcm3.

Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such​ data, would a brain volume of

1287.01287.0

cm cubedcm3

be significantly​ high?

Answer 1

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Answer:

Given that the brain volumes of 20 brains have a mean of 1059.2 cm³ an standard deviation of 128.9 cm³.

Range rule of thumb says that the Range is four times the standard deviation. So we say that the usual values will be 2 standard deviations away from the mean of the data distribution.

In any distribution with mean and standard deviation known the usual values lie with in mean - 2*standard deviation and mean + 2*standard deviation.

If the data point is less than mean - 2* standard deviation then we say that it is significantly low.

If the data point is greater than mean + 2*standard deviation then we say that it is significantly high.

Assume xbar is mean and s is standard deviaiton

Given mean is 1059.2 cm³ and standard deviation is 128.9 cm³. We calcualte the boundaries for usual values of 20 brains is shown below

x = 1059.2

SD = 128.9

Lower boundary = x - 2SD = 1059.2 - 2*128.9 = 801.4

Upper boundary = x + 2SD = 1059.2 + 2*128.9 = 1317

All values below 801.4 are considered to be significantly low and all values above 1317 are considered to be significantly high.

The given value 1287.0 is less than the upper boundary, So we say it does not have significantly high value.