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%.

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:

[tex]S\approx \frac{2.76}{4}= 0.690[/tex]

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

[tex]\frac{0.117}{0.807} \times 100= 14.50\%[/tex].

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