Question

The brain volumes (cm3 ) of 50 brains vary from a low of 916cm³ to a high of 1492cm³. Use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of 181.5cm³, assuming the estimate is accurate if it is within 15cm³. What is the estimate standard deviation?

Compare the result to the exact standard deviation. Fill in the blank.

The approximation (is/is not) accurate because the error range rule of thumb is (less than/greater than) 15cm³

Answer 1

Answer:

Given exact standard deviation = 181.5

181.5 - 15 = 166.5

181.5 + 15 = 196.5

Within 15 cm3 from exact standard deviation means between 166.5 and 196.5cm3.

The estimate

The range rule of thumb says that the standard deviation is approximately one-fourth the range.

Given Min = 916 and Max = 1492

Range = Max - Min = 1492 - 916 = 576

Standard deviation = Range/4 = 576/4 = 144

Since 144 does not lie between 166.5 and 196.5 cm3 (within 15 cm3 from exact standard deviation), the estimate is NOT accurate.

The approximation is not accurate because the error range rule of thumb is lgreater than) 15cm3

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