Q 3.87. - Elementary Statistics

Question

In each Exercises 3.82-3.90, use the technology of your choice to determine and interpret the range and sample standard deviation for those data sets to which those concepts apply. If those concepts don't apply, explain why. Note: If an exercise contains more than one data set, perform the aforementioned tasks for each data set.

The Beatles. In the article. "Length of The Beatles' Songs" (Chance, Vol. 25, No. 1. pp . 30-33), T. Koyama discusses aspects and interpretations of the lengths of songs by The Beatles. Data on the length, in seconds, of 229 Beatles' songs are presented on the WeissStats site.

Step-by-Step Solution

Answer

Range 470.

Standard deviation 57.57.

Step 1. Given information.

The given statement is: 

The WeissStats website has information on the length of 229 Beatles songs in seconds.

Step 2. Use MINITAB for the calculation of range and sample standard deviation.

MINITAB can be used to calculate the range and standard deviation. Procedure for MINITAB:

Step 1: Select Stat > Basic Statistics > Display Descriptive Statistics from the drop-down menu.

Step 2: In the Variables section, type LENGTH.

Step 3: Select Range, minimum, maximum, and standard deviation from the statistics menu.

Step 4: Click the OK button.

MINITAB OUTPUT:

Descriptive Statistics: LENGTH

$$\begin{gathered} \mathrm{Variable} \mathrm{N} {\mathrm{N}}^{*} \mathrm{St} \mathrm{Dev} \mathrm{Minimum} \mathrm{Maximum} \mathrm{Range} \\ \mathrm{LENGTH} 229 0 57.57 23.00 493.00 470.00 \end{gathered}$$

The range and standard deviation for "LENGTH" are 470 and 57.57, respectively, according to the MINITAB output. 

Step 3. Interpretation of the range and sample standard deviation.

There is a 470-point variance between the maximum and least values.

The data value and the average are separated by 57.57. The difference between the total number of LENGTH and the average number of pups is 57.57.