Question

Write three functions that compute the mean, median, and mode, respectively, of a list of values. For each local variable you use. indicate its role using comments. Don't forget to identify the role of variables you use in loops. Use the following to get started:

Short answer

Define three functions for mean, median, mode: use summation and division for mean, sorting for median, and frequency count for mode.

Step-by-step solution

Write the function to calculate the mean

Start by defining a function named `calculate_mean` that accepts a list of values as an argument. Initialize a variable `total_sum` to 0, which will be used to store the sum of all values. Loop through each number in the list, adding it to `total_sum`. Once done, divide `total_sum` by the number of items in the list (i.e., its length), and save this result in a variable called `mean`. Return `mean` at the end of the function.

Write the function to calculate the median

Define a function named `calculate_median` that takes a list of numbers as input. Sort the list and assign it to a variable named `sorted_values`. Compute the length of the list, storing it in a variable `n`. Determine if `n` is odd or even. For odd, use the middle number (i.e., `sorted_values[n // 2]`) and save it in a variable, `median`. For even, calculate the average of the two middle numbers and store it in `median`. Finally, return `median`.

Write the function to calculate the mode

Create a function called `calculate_mode` that accepts a list of numbers. Initialize a dictionary `frequency` to count the occurrences of each number. Loop through the list, updating the count for each number in `frequency`. Identify the number(s) with the highest count by checking the values and store the result in a variable called `mode`. If there is more than one number with the highest count, include all of them in `mode`. Return `mode` as a list.

Key concepts

Mean Calculation

When working with a list of numbers in Python, calculating the mean is a fundamental statistical operation. The mean, also known as the average, provides a central value of the dataset. To compute the mean, follow these basic steps:
First, sum up all the numbers in the list using a loop or built-in Python functions. This total is stored in a variable, commonly named `total_sum`.
Next, divide this total by the count of numbers in the list, often obtained using the `len()` function to determine the list's length. The result is stored in another variable, `mean`. This operation essentially spreads the total evenly across all data points.
The Python function for this might look like this:

• Initialize `total_sum` to 0.
• Loop over each number, adding it to `total_sum`.
• Compute `mean` as `total_sum` divided by the list's length.
• Return the `mean`.

This approach provides a simple and efficient way to calculate the mean, offering a snapshot of your data spread.

Median Calculation

The median is another way to find the central value of a dataset, especially useful when the data contains outliers. To calculate the median in Python, follow these steps:
First, sort the list to arrange the numbers in ascending order. You can use Python's `sorted()` function for this.
Once sorted, determine the length of the list to check whether it is odd or even. This decision is crucial as it dictates whether you'll pick a single middle value or take the average of two middle values.
If the count of numbers is odd, simply locate the middle element. This is found at the index `n // 2` where `n` is the length.
If the count is even, find the two middle elements and calculate their average.
The steps in a function would be:

• Sort the list of numbers.
• Check if the length is odd or even.
• If odd, pick the middle value; if even, average the two middle values.
• Return this value as the median.

This way, the median provides a more robust central point that isn't skewed by extreme values.

Mode Calculation

Calculating the mode involves identifying the number that appears most frequently in a dataset. In cases where data points repeat, the mode gives insight into the most common values within your data.
To determine the mode in Python, follow these steps:
Start by creating a dictionary to keep track of the frequency of each number. As you loop through the list, increment the count for each number in this dictionary.
After populating the dictionary, identify which number(s) have the highest occurrence. If multiple numbers have the same maximum frequency, all are considered modes.
The function can be structured as follows:

• Initialize an empty dictionary `frequency`.
• Iterate through the list, updating frequencies.
• Determine the highest frequency value(s).
• Return the number(s) corresponding to this frequency as the mode.

This method of mode calculation is especially useful in cases where you need to analyze repeating patterns or trends in your dataset.