This Python function, `calculate_average`, computes the average of a list of numbers. It first checks if the list is empty. If the list contains numbers, it calculates the average by dividing the sum of the numbers, found using the built-in `sum()` function, by the count of the numbers, determined by the `len()` function. To prevent a `ZeroDivisionError`, the function returns 0 if the input list is empty.

```python
def calculate_average(numbers):
    """
    Calculates the average of a list of numbers.
    Returns 0 if the list is empty.
    """
    if numbers: # Check if the list is not empty
        return sum(numbers) / len(numbers)
    else:
        return 0

# Example 1: Non-empty list
my_numbers = [10, 20, 30, 40, 50]
average = calculate_average(my_numbers)
print(f"The average is: {average}")
# Expected Output: The average is: 30.0

# Example 2: Empty list
empty_list = []
average_empty = calculate_average(empty_list)
print(f"The average of an empty list is: {average_empty}")
# Expected Output: The average of an empty list is: 0
```

Python Function to Calculate the Average of a List

• Mean: The "average" number; found by adding all data points and dividing by the number of data points.

• Median: The middle number; found by ordering all data points and picking out the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).

• Mode: The most frequent number—that is, the number that occurs the highest number of times.


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• mean

• median

• mode

• percentiles

• range

• variance

• standard deviation

• mean squared error

• consistency

statistical measures

Reference of Foundations of Large Language Models Course

mean, median and mode

• Variance: The variance of the data is the average squared distance between the mean and each data value.

• Standard deviation: Standard deviation is calculated as the square root of the variance (the average squared deviation from the mean).



variance and standard deviation

Mean Squared Error is simply the variance of a potentially biased estimator $\hat{\theta}_m$ of the Expected Value or Mean $\theta$
$$MSE(\hat{\theta}_m) = \mathbb{E}((\hat{\theta}_m - \theta)^2)$$
$$ = Bias^2(\hat{\theta}_m) + Var(\hat{\theta}_m)$$

Mean Squared Error

In statistics, consistency is a property of an estimator where its probabilistic limit converges to the true underlying parameter value as the sample size approaches infinity ($$	ext{plim}_{mightarrow\infty}\hat{	heta}_m=	heta$$). When an estimator is consistent, accumulating more data guarantees that empirical estimates will eventually match the true theoretical probabilities.

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