Questions: Describe why the range might not be the best measure of dispersion. Choose the correct answer below. A. The range is a quick but rough measure of dispersion. It is the difference between the highest and lowest data values in a data set. On the other hand, the standard deviation is a measure of dispersion that is dependent on all of the data items, and therefore is generally more useful. B. The range is a quick but rough measure of dispersion. It is found by determining how much each data item differs from the mean. On the other hand, the standard deviation is a measure of dispersion that is found by determining how much each data item differs from the median, and therefore is generally more usefut. C. The range is a quick but rough measure of dispersion. It is found by determining how much each data item differs from the mean, but is not dependent on all of the data items. Similarly, the standard deviation is also found by determining how much each data item differs from the mean, but is a measure of dispersion that is dependent on all of the data items and therefore is generally more useful. D. The range is a quick but rough measure of dispersion. It is dependent on all of the data items. On the other hand, the standard deviation is the difference between the highest and lowest data values in a data set, and therefore is generally more useful.

Describe why the range might not be the best measure of dispersion. Choose the correct answer below. A. The range is a quick but rough measure of dispersion. It is the difference between the highest and lowest data values in a data set. On the other hand, the standard deviation is a measure of dispersion that is dependent on all of the data items, and therefore is generally more useful. B. The range is a quick but rough measure of dispersion. It is found by determining how much each data item differs from the mean. On the other hand, the standard deviation is a measure of dispersion that is found by determining how much each data item differs from the median, and therefore is generally more usefut. C. The range is a quick but rough measure of dispersion. It is found by determining how much each data item differs from the mean, but is not dependent on all of the data items. Similarly, the standard deviation is also found by determining how much each data item differs from the mean, but is a measure of dispersion that is dependent on all of the data items and therefore is generally more useful. D. The range is a quick but rough measure of dispersion. It is dependent on all of the data items. On the other hand, the standard deviation is the difference between the highest and lowest data values in a data set, and therefore is generally more useful.
Transcript text: Describe why the range might not be the best measure of dispersion. Choose the correct answer below. A. The range is a quick but rough measure of dispersion. It is the difference between the highest and lowest data values in a data set. On the other hand, the standard deviation is a measure of dispersion that is dependent on all of the data items, and therefore is generally more useful. B. The range is a quick but rough measure of dispersion. It is found by determining how much each data item differs from the mean. On the other hand, the standard deviation is a measure of dispersion that is found by determining how much each data item differs from the median, and therefore is generally more usefut. C. The range is a quick but rough measure of dispersion. It is found by determining how much each data item differs from the mean, but is not dependent on all of the data items. Similarly, the standard deviation is also found by determining how much each data item differs from the mean, but is a measure of dispersion that is dependent on all of the data items and therefore is generally more useful. D. The range is a quick but rough measure of dispersion. It is dependent on all of the data items. On the other hand, the standard deviation is the difference between the highest and lowest data values in a data set, and therefore is generally more useful.
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Solution

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Solution Steps

Step 1: Calculate the Mean

The mean \( \mu \) of the dataset is calculated as follows:

\[ \mu = \frac{\sum x_i}{n} = \frac{144}{8} = 18.0 \]

Step 2: Calculate the Variance

The variance \( \sigma^2 \) is computed using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} = 27.43 \]

Step 3: Calculate the Standard Deviation

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{27.43} = 5.24 \]

Step 4: Discuss the Range and Standard Deviation

The range is defined as the difference between the highest and lowest data values in a dataset. It is a quick but rough measure of dispersion. In contrast, the standard deviation is a measure of dispersion that takes into account all data items, making it generally more useful.

Final Answer

The range is a quick but rough measure of dispersion. It is the difference between the highest and lowest data values in a data set. On the other hand, the standard deviation is a measure of dispersion that is dependent on all of the data items, and therefore is generally more useful.

The answer is A.

\(\boxed{A}\)

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