Let's break down the required calculations: arithmetic mean, average deviation, and standard deviation.

Step 1: Arithmetic Mean

The arithmetic mean is the sum of all the values divided by the number of values.

Given values:
$12.35, 12.71, 12.48, 10.24, 12.63, 12.58$

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

Where:

• $\sum x_i$ is the sum of all the data points
• $n$ is the number of data points

$\mu = \frac{12.35 + 12.71 + 12.48 + 10.24 + 12.63 + 12.58}{6}$

Step 2: Average Deviation

The average deviation is the mean of the absolute differences between each value and the arithmetic mean.

Average deviation $AD = \frac{\sum |x_i - \mu|}{n}$

Where:

• $x_i$ is each individual value
• $\mu$ is the arithmetic mean

Step 3: Standard Deviation

The standard deviation measures the spread of the data values relative to the mean.

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

Where:

• $x_i$ is each individual value
• $\mu$ is the arithmetic mean

Let me calculate all of these values for you.