Question

The brain volumes (cm³) of 50 brains vary from a low of 906 cm³ to a high of 1498 cm³. Use the range rule of thumb to estimate the standard deviations and compare the result to the exact standard deviation of 171 cm³, assuming the estimate is accurate if it is within 15 cm³.

The estimated standard deviation is ​

Answer 1

The range rule of thumb suggests that the estimated standard deviation is approximately 18.2 cm³. This estimate is within 15 cm³ of the exact standard deviation of 171 cm³, indicating that it is accurate.

Answer 2

Explanation:

The range of the brain volumes is:

Range = highest value - lowest value = 1498 cm³ - 906 cm³ = 592 cm³

According to the range rule of thumb, the standard deviation can be estimated as:

Standard deviation ≈ Range / 4

Standard deviation ≈ 592 cm³ / 4 ≈ 148 cm³

The estimate of the standard deviation is within 15 cm³ of the exact standard deviation of 171 cm³, so it can be considered accurate according to the given criteria. However, note that the range rule of thumb is a very rough estimate and may not be very accurate in all cases.