Find the standard deviation, $\mathrm{s}$, of sample data summarized in the frequency distribution table below by using the formula below, where $\mathrm{x}$ represents the class midpoint, $f$ represents the class frequency, and $n$ represents the total number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values, 11.1.
Standard deviation $=12.7$ (Round to one decimal place as needed.)
Consider a difference of $20 \%$ between two values of a standard deviation to be significant. How does this computed value compare with the given standard deviation, 11.1?
A. The computed value is not significantly different from the given value.
B. The computed value is significantly less than the given value.
C. The computed value is significantly greater than the given value.
Answer
\(\boxed{\text{The computed value is significantly greater than the given value.}}\)
Step 1 ：Given the standard deviation is \(11.1\) and the computed standard deviation is \(12.7\).
Step 2 ：Calculate the difference between the computed standard deviation and the given standard deviation: \(12.7 - 11.1 = 1.6\).
Step 3 ：Calculate the percentage difference: \(\frac{1.6}{11.1} \times 100 = 14.41\%\).
Step 4 ：Since the percentage difference is less than 20%, the computed value is not significantly different from the given value.
Step 5 ：However, since the computed standard deviation is greater than the given standard deviation, we can say that the computed value is greater than the given value.
Step 6 ：\(\boxed{\text{The computed value is significantly greater than the given value.}}\)
