Let's go through the steps to calculate both the standard deviation and the coefficient of variation for the dataset:

Data: $99, 65, 54, 81, 77, 60, 77, 50, 51, 47, 88, 44, 57, 64, 77$

1. Mean ($\bar{x}$): Calculate the mean of the data.

   $\bar{x} = \frac{\sum x}{n} = \frac{99 + 65 + 54 + 81 + 77 + 60 + 77 + 50 + 51 + 47 + 88 + 44 + 57 + 64 + 77}{15}$

2. Variance ($\sigma^2$): Find the variance by calculating the average of the squared differences from the mean.

   $\sigma^2 = \frac{\sum (x - \bar{x})^2}{n}$

3. Standard Deviation ($\sigma$): Take the square root of the variance to get the standard deviation.

   $\sigma = \sqrt{\sigma^2}$

4. Coefficient of Variation (CV): This is the ratio of the standard deviation to the mean, expressed as a percentage.

   $\text{CV} = \left( \frac{\sigma}{\bar{x}} \right) \times 100\%$

Let me perform these calculations.The calculations yield the following results:

• Mean: $66.07$
• Standard Deviation: $15.82$
• Coefficient of Variation (CV): $23.94\%$

Would you like more details on any part of this calculation?

Here are five follow-up questions to deepen your understanding:

1. How does the coefficient of variation help in comparing variability across different datasets?
2. What would the standard deviation look like if the data had a larger range of values?
3. How does changing one data point affect the mean and standard deviation?
4. What is the difference between population and sample standard deviation?
5. How can we use the standard deviation in real-world applications?

Tip: Remember, the coefficient of variation is particularly useful for comparing relative variability between datasets with different units or means.