To calculate the standard deviation and the coefficient of variation for the dataset, let's proceed with the following steps:

1. Calculate the mean of the dataset.
2. Calculate the variance by finding the average of the squared deviations from the mean.
3. Determine the standard deviation by taking the square root of the variance.
4. Calculate the coefficient of variation (CV) by dividing the standard deviation by the mean and expressing it as a percentage.

Let's proceed with each step:

Data:

$94, 78, 58, 82, 79, 62, 82, 54, 52, 45, 82, 48, 55, 67, 66$

Step 1: Calculate the Mean

$\text{Mean} = \frac{\sum \text{Data Points}}{\text{Number of Data Points}}$

Step 2: Calculate the Variance

$\text{Variance} = \frac{\sum (x_i - \text{Mean})^2}{N}$

Step 3: Calculate the Standard Deviation

$\text{Standard Deviation} = \sqrt{\text{Variance}}$

Step 4: Calculate the Coefficient of Variation

$\text{Coefficient of Variation (CV)} = \left(\frac{\text{Standard Deviation}}{\text{Mean}}\right) \times 100\%$

I'll calculate these values.The calculations yield the following results:

• Mean: $66.93$
• Standard Deviation: $14.51$
• Coefficient of Variation (CV): $21.68\%$

The coefficient of variation shows the degree of variability in relation to the mean of the dataset.

Would you like a detailed breakdown of each calculation step, or do you have any questions?

Here are some related questions to further explore:

1. How is the coefficient of variation useful in comparing datasets with different units?
2. What does a high or low coefficient of variation indicate about the data?
3. Can the coefficient of variation be negative, and under what circumstances?
4. How does the sample standard deviation differ from the population standard deviation?
5. What are the applications of standard deviation and CV in real-world data analysis?

Tip: The coefficient of variation is especially useful for comparing variability between datasets with different means or units.