Let's start by calculating the mean and standard deviation of the given numbers.

Numbers:

48,493
43,154
26,707
37,052
33,379
40,121
40,633
37,598
25,084
33,267
38,161
38,616
33,704
38,443
37,602
44,330

1. Mean (Average):

The formula for the mean is: $\text{Mean} = \frac{\sum x_i}{n}$ Where:

• $\sum x_i$ is the sum of all numbers
• $n$ is the total number of numbers

2. Standard Deviation:

The formula for the standard deviation is: $\text{Standard Deviation} = \sqrt{\frac{\sum (x_i - \mu)^2}{n}}$ Where:

• $x_i$ are the individual numbers
• $\mu$ is the mean
• $n$ is the total number of numbers

Let me calculate the values for you.

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Calculation of Mean and Standard Deviation:

1. First, sum all the numbers: $48,493 + 43,154 + 26,707 + 37,052 + 33,379 + 40,121 + 40,633 + 37,598 + 25,084 + 33,267 + 38,161 + 38,616 + 33,704 + 38,443 + 37,602 + 44,330$

2. Then, divide by the number of elements (16 numbers): $\text{Mean} = \frac{ \text{sum of numbers} }{16}$

3. To find the standard deviation, subtract the mean from each number, square the differences, sum them, and then divide by 16, and finally take the square root.

Let me perform these calculations. numpy as np

List of numbers

numbers = [ 48493, 43154, 26707, 37052, 33379, 40121, 40633, 37598, 25084, 33267, 38161, 38616, 33704, 38443, 37602, 44330 ]

Calculating mean and standard deviation

mean = np.mean(numbers) std_dev = np.std(numbers)

mean, std_devThe mean of the given numbers is 37,271.5, and the standard deviation is approximately 5,799.04.

Would you like further details on how these were calculated or have any other questions?

Here are some related questions for you:

1. How can the standard deviation help you understand the distribution of data?
2. What is the difference between population and sample standard deviation?
3. How would you calculate the variance from the standard deviation?
4. How can you visualize the distribution of these numbers using a histogram?
5. What does a high standard deviation indicate about the spread of the data?

Tip: When working with large datasets, consider using software or a calculator to automate the process of calculating the mean and standard deviation, especially for more complex datasets!