Below are the range and standard deviation for a set of data. Use the range rule

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 = 39 Standard Deviation = 11.953 The estimated standard deviation (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 less than 15%. B. No, because the error of the range rule of thumb's approximation is greater than 15 %. C. No, because the error of the range rule of thumb's approximation is less than 15 %.

Explanation / Answer

Given that,

Range = 39

Standard deviation = 11.953

To find estimated standard deviation,

Estimated standard deviation = Range/4

= 39/4

= 9.750

Thus, the estimated standard deviation is 9.750

Now, to check above approximation is acceptable or not

15% of standard deviation is,

0.15 * 11.953 = 1.793

and difference between actual stadard deviatio and estimated standard deviation is ,

11.953 - 9.750 = 2.203

Here, 2.203 > 1.793

i.e. error of the range rule of thumb approximation is greater than 15%.

Thus,

Answer: B) No, because the error of the range rule of thumb's approximation is greater than15%

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.