Answer:
The Range Rule of Thumb says that the range is about four times the standard deviation. So, if you need to calculate it, you need to divide range (Maximum - Minimum) with 4, S=[tex]\frac{R}{4}[/tex].
Step-by-step explanation:
R=1490 - 904
S = 586 / 4 = 149.5
If you compare the exact standard desviation (149.5 cm) with the estimated (146.5 cm), it is a difference of 3 cm, is not neccesary round the result.
Hope my answer has been useful.
Answer:
x_bar = 1197 cm^3 , s.d_e = 146.5 cm^3
Outside the 15 cm^3 tolerance. Not a good estimation.
Step-by-step explanation:
Given:
- Lowest value of brain volume L = 904 cm^3
- Highest value of brain volume H = 1490 cm^3
- Exact standard deviation s.d_a = 174.7 cm^3
Find:
Use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of 174.7 cm^3 assuming the estimate is accurate if it is within 15 cm^3.
Solution:
- The rule of thumb states that the max and min limits are +/- 2 standard deviations about the mean x_bar. Hence, we will set up two equations.
L = x_bar - 2*s.d_e
H = x_bar + 2*s.d_e
Where, s.d_e is the estimated standard deviation.
- Solve the two equations simultaneously and you get the following:
x_bar = 1197 cm^3 , s.d_e = 146.5 cm^3
- The exact standard deviation is s.d_a = 174.7 cm^3
So, the estimates differs by:
s.d_a - s.d_e = 174.7 - 146.5 = 28.2 cm^3
Hence, its outside the tolerance of 15 cm^3. Not a good approximation.
