To calculate the coefficient of variation (CV) for each set of data, we use the following formula:

$CV = \left( \frac{\sigma}{\mu} \right) \times 100$

Where:

• $\sigma$ is the standard deviation of the data set.
• $\mu$ is the mean of the data set.

Step-by-step process:

1. Calculate the mean ($\mu$): The mean is the sum of all values in the data set divided by the number of values.

   $\mu = \frac{\sum x_i}{n}$

   Where $x_i$ are the data points and $n$ is the number of data points.

2. Calculate the standard deviation ($\sigma$): The standard deviation is calculated as:

   $\sigma = \sqrt{\frac{1}{n} \sum (x_i - \mu)^2}$

3. Plug the values into the CV formula.

Now, let’s go through this calculation for both sets of data:

---

Data Set A:

Data:
20,40720,407, 20,14520,145, 20,36320,363, 20,12420,124, 21,17721,177, 21,46521,465, 22,19422,194, 20,83420,834, 21,71721,717, 21,61321,613, 21,61921,619, 21,22321,223, 20,53220,532, 21,19521,195

This data set appears to have large numbers that seem repeated (like 20,40720,407). I believe there may be a typo or formatting issue. Please confirm if this is the intended data or provide the correct values.

---

Data Set B:

Data: 4.26, 4.00, 4.01, 4.14, 3.60, 4.58, 2.94, 3.81, 3.78, 2.98, 3.50

Let's proceed with Data Set B first since it’s formatted correctly.

Step 1: Calculate the mean ($\mu$) for Data Set B.

$\mu = \frac{4.26 + 4.00 + 4.01 + 4.14 + 3.60 + 4.58 + 2.94 + 3.81 + 3.78 + 2.98 + 3.50}{11}$

$\mu = \frac{41.60}{11} = 3.782$

Step 2: Calculate the standard deviation ($\sigma$) for Data Set B.

$\sigma = \sqrt{\frac{1}{11} \sum (x_i - \mu)^2}$

Calculating the squared differences from the mean:

(4.00 - 3.782)^2 = 0.047 \\ (4.01 - 3.782)^2 = 0.051 \\ (4.14 - 3.782)^2 = 0.126 \\ (3.60 - 3.782)^2 = 0.033 \\ (4.58 - 3.782)^2 = 0.635 \\ (2.94 - 3.782)^2 = 0.711 \\ (3.81 - 3.782)^2 = 0.0008 \\ (3.78 - 3.782)^2 = 0.000004 \\ (2.98 - 3.782)^2 = 0.640 \\ (3.50 - 3.782)^2 = 0.079 \\$$ Sum of squared differences: $$0.230 + 0.047 + 0.051 + 0.126 + 0.033 + 0.635 + 0.711 + 0.0008 + 0.000004 + 0.640 + 0.079 = 2.5028$$ Now, calculate the standard deviation: $$\sigma = \sqrt{\frac{2.5028}{11}} = \sqrt{0.2275} = 0.477$$ #### Step 3: Calculate the coefficient of variation (CV) for Data Set B. $$CV = \left( \frac{0.477}{3.782} \right) \times 100 = 12.6\%$$ --- **Summary for Data Set B:** - Mean ($$\mu$$): 3.782 - Standard Deviation ($$\sigma$$): 0.477 - Coefficient of Variation (CV): **12.6%** --- Let me know if you'd like me to proceed with calculating the coefficient of variation for Data Set A after you confirm the correct values, or if you need further clarifications!