Question

Below are the range and standard deviation for a set of data. Use the range rule of thumb and compare it to the standard deviation listed below. Does the range rule of thumb produce an acceptable​ approximation? Suppose a researcher deems the approximation as acceptable if it has an error less than​ 15%. Range equals 2.76 standard deviation equals 0.807 the estimated standard deviation is nothing. ​(round to three decimal places as​ needed.) is this an acceptable​ approximation?
a. Yes​, because the error of the range rule of​ thumb's approximation is greater than​ 15%.
b. No​, because the error of the range rule of​ thumb's approximation is less than​ 15%.
c. Yes​, because the error of the range rule of​ thumb's approximation is less than​ 15%.
d. No​, because the error of the range rule of​ thumb's approximation is greater than​ 15%.

Answer 1

Solution: We are given:

$Range =2.76$

$Standard-deviation=0.807$

Now let's find the estimated value of standard deviation using the range rule of thumb. According to range rule of thumb, the estimate of standard deviation is:

$S\approx \frac{2.76}{4}= 0.690$

Therefore the estimated standard deviation is 0.690

is this an acceptable​ approximation?

Answer: c. Yes​, because the error of the range rule of​ thumb's approximation is less than​ 15%.

Explanation:

The difference between estimated standard deviation and actual standard deviation is:

0.807 - 0.690 = 0.117

Now let's find the percentage of error

$\frac{0.117}{0.807} \times 100= 14.50\%$.

Therefore, the error of the range rule of​ thumb's approximation is less than​ 15%.