To calculate the standard deviation and the coefficient of variation for the dataset, we proceed as follows:

Step 1: Mean Calculation

First, we find the mean (average) of the data.

Given dataTo calculate the standard deviation and the coefficient of variation for the dataset, we proceed as follows:

Step 1: Mean Calculation

First, we find the mean (average) of the data.

Given $70, 58, 61, 86, 61, 86, 59, 66, 91, 73, 64, 66, 77, 66, 55$

The mean, $\bar{x}$, is calculated by: $\bar{x} = \frac{\sum x_i}{n}$ where $n$ is the number of data points.

Step 2: Variance Calculation

The variance, $\sigma^2$, is calculated by: $\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}$ Then, the standard deviation, $\sigma$, is the square root of the variance: $\sigma = \sqrt{\sigma^2}$

Step 3: Coefficient of Variation (CV)

The coefficient of variation is calculated by: $\text{CV} = \frac{\sigma}{\bar{x}} \times 100\%$

Let's proceed with these calculations.Here are the results for the dataset:

1. Mean (Average): $69.27$
2. Standard Deviation: $10.77$
3. Coefficient of Variation (CV): $15.54\%$

The coefficient of variation indicates the relative variability of the dataset in percentage terms.

Would you like further details on these calculations, or do you have any questions?

Here are some related questions to consider:

1. How does the coefficient of variation help in comparing datasets?
2. What is the significance of a high versus low coefficient of variation?
3. How would the standard deviation change if we added more outliers to the dataset?
4. How can we use standard deviation to understand data spread?
5. What are some real-world applications of the coefficient of variation?

Tip: The coefficient of variation is especially useful when comparing the relative variability of two datasets with different means.