## Calculating Average Values in Python: np.mean() vs. np.average()

Are you working with an array of data in Python and need to calculate the average value?

Fortunately, Python provides two convenient functions to do just that – np.mean() and np.average(). In this article, we’ll dive into the similarities and differences between these two functions and how to use them effectively.

First, let’s define what we mean by “average value.” In statistics, the most common type of average is the arithmetic mean. This is simply the sum of all the values divided by the number of values.

For example, if we had an array of [2, 4, 6, 8], the arithmetic mean would be (2+4+6+8)/4, which is 5. Another type of average is the weighted average.

This takes into account the importance or relevance of each value. For instance, if we had an array of [2, 4, 6, 8], but the value of 8 was more important, we might weigh it twice as much.

The weighted average in this case would be (2*1 + 4*1 + 6*1 + 8*2)/(1+1+1+2), which is 6. Now, let’s take a look at how np.mean() and np.average() handle these two types of averages.

### np.mean()

The np.mean() function returns the arithmetic mean of an array of values. Here’s the basic syntax:

```
import numpy as np
data = [2, 4, 6, 8]
average = np.mean(data)
```

In this example, np.mean() takes the array data and calculates its arithmetic mean, which is then assigned to the variable “average.”

But np.mean() can also handle multi-dimensional arrays. For example:

```
import numpy as np
data = [[2, 4, 6], [8, 10, 12]]
average = np.mean(data)
```

In this case, np.mean() calculates the arithmetic mean of all the values in the matrix by summing them up and dividing by the total number of values.

### np.average()

The np.average() function can also calculate the arithmetic mean, but it also allows you to specify weights for each value.

Here’s the basic syntax:

```
import numpy as np
data = [2, 4, 6, 8]
weights = [1, 1, 1, 2]
average = np.average(data, weights = weights)
```

In this example, np.average() takes the array data and the array of weights, and calculates the weighted average. The value of 8, which has a weight of 2, will contribute more to the final average than the other values.

But what if we just want to calculate the arithmetic mean? In that case, we can leave out the weights parameter:

```
import numpy as np
data = [2, 4, 6, 8]
average = np.average(data)
```

In this example, np.average() will still calculate the arithmetic mean since no weights were specified.

## Similarities and Differences

### Similarities:

- Both functions can be used for calculating the arithmetic mean.
- Both functions can handle multi-dimensional arrays.

### Differences:

- np.average() allows you to specify weights for each value, while np.mean() does not.
- If weights are not specified, np.average() will still calculate the arithmetic mean, while np.mean() always calculates the arithmetic mean.

## Example Usage

### Example 1: Using np.mean()

```
import numpy as np
data = [2, 4, 6, 8]
average = np.mean(data)
print("The arithmetic mean is:", average)
```

Output: The arithmetic mean is: 5.0

### Example 2: Using np.mean() with a multi-dimensional array

```
import numpy as np
data = [[2, 4, 6], [8, 10, 12]]
average = np.mean(data)
print("The arithmetic mean is:", average)
```

Output: The arithmetic mean is: 7.0

### Example 3: Using np.average() with weights

```
import numpy as np
data = [2, 4, 6, 8]
weights = [1, 1, 1, 2]
average = np.average(data, weights = weights)
print("The weighted average is:", average)
```

Output: The weighted average is: 6.0

### Example 4: Using np.average() to calculate the arithmetic mean

```
import numpy as np
data = [2, 4, 6, 8]
average = np.average(data)
print("The arithmetic mean is:", average)
```

Output: The arithmetic mean is: 5.0

## Conclusion

In conclusion, np.mean() and np.average() are both useful functions for calculating average values in Python. However, np.mean() is simpler and faster when only an arithmetic mean is required.

On the other hand, if you need to take into account the relative importance of each value, then np.average() with weights is the way to go. Knowing these differences will help you choose the best function for your calculations.

### Example 2: Using np.average() with Weights

In the previous section, we saw how np.average() allows us to calculate the weighted average of an array of values. Let’s take a closer look at how to supply weights to np.average().

When using np.average() with weights, we need to provide a list of values that correspond to the weights of each element in the array. This list must have the same length as the array:

```
import numpy as np
data = [2, 4, 6, 8]
weights = [1, 1, 1, 2]
average = np.average(data, weights=weights)
```

In this example, we have an array of values “data” and a list of weights “weights”. The weights indicate how important each value is, with a weight of 2 for the value of 8.

We pass both data and weights to np.average(), along with the “weights” parameter. The “weights” parameter can also take the form of a multi-dimensional array.

This allows us to specify weights for multiple variables, which can be useful for more advanced statistical analysis. For example:

```
import numpy as np
data = [[1, 2, 3], [4, 5, 6]]
weights = [[0.1, 0.2, 0.3], [0.4, 0.5, 0.6]]
average = np.average(data, weights=weights)
```

In this example, we have two vectors of values “data”, with corresponding weights “weights”. The weights are now specified as a two-dimensional array, where each row represents the weights for one vector.

When using np.average() with weights, it’s important to note that the sum of the weights must be equal to one. This is because the function calculates the weighted average as the sum of the products of the values and their corresponding weights, divided by the sum of the weights.

If the weights do not add up to one, the resulting average will be incorrect. For instance, consider the following example:

```
import numpy as np
data = [2, 4, 6, 8]
weights = [1, 1, 1, 3]
average = np.average(data, weights=weights)
```

In this example, the weights add up to 6 instead of 4. The resulting average will be calculated as (2*1 + 4*1 + 6*1 + 8*3)/(1+1+1+3+1), which is 6.2 instead of 6.

### Summary of np.mean() and np.average()

To summarize, np.mean() and np.average() are two functions in NumPy that allow us to calculate the average value of an array. The main difference between the two functions is that np.average() allows us to provide weights for each value, while np.mean() assumes that all values have the same importance.

When calculating the weighted average using np.average(), we need to provide a list of weights that correspond to each value in the array. The sum of the weights must be equal to one, or the resulting average will be incorrect.

## Reference to NumPy Documentation

For further information on np.mean() and np.average(), consult the official NumPy documentation at https://numpy.org/doc/stable/reference/generated/numpy.mean.html and https://numpy.org/doc/stable/reference/generated/numpy.average.html. There, you’ll find detailed explanations of the syntax, parameters, and examples of how to use these functions in various situations.

The documentation also covers other useful functions for working with arrays and matrices in Python, such as np.sum(), np.product(), and np.std(). In conclusion, np.mean() and np.average() are powerful tools in Python that allow us to calculate average values of arrays and matrices.

np.mean() calculates the arithmetic mean of an array, while np.average() calculates a weighted average based on the relative importance of each value. To use np.average() with weights, we need to provide a list of weights that correspond to each value in the array and ensure that the weights add up to one.

With the knowledge of these functions, data scientists and Python developers can perform advanced statistical analysis with ease. Remember to consult the NumPy documentation for more information and examples.