Mean, Median, and Mode in Python

In statistics, the mean, median, and mode are measures of central tendency that describe the center of a data distribution. You can easily calculate these using Python's built-in functions or libraries such as statistics.

1. Mean

The mean (or average) is the sum of all values divided by the number of values.

Formula:

Where:

• $x_i$ is each individual value

• $n$ is the number of values

Example: Calculating Mean in Python

import statistics# Datadata = [1, 2, 3, 4, 5]# Calculate meanmean_value = statistics.mean(data)print("Mean:", mean_value)

2. Median

The median is the middle value of a dataset when the values are sorted in ascending order. If the number of values is even, the median is the average of the two middle values.

Steps to find the median:

1. Sort the data.

2. If the number of values is odd, the median is the middle value.

3. If the number of values is even, the median is the average of the two middle values.

Example: Calculating Median in Python

import statistics# Datadata = [1, 2, 3, 4, 5]# Calculate medianmedian_value = statistics.median(data)print("Median:", median_value)

3. Mode

The mode is the value that appears most frequently in a dataset. If there are multiple values that appear with the same highest frequency, the dataset is multimodal. If no number repeats, the dataset has no mode.

Example: Calculating Mode in Python

import statistics# Datadata = [1, 2, 2, 3, 4, 5]# Calculate modemode_value = statistics.mode(data)print("Mode:", mode_value)

Handling Multimodal Data

If your dataset has more than one mode, the statistics.mode() function will raise an error. To handle multimodal data (where there are multiple modes), you can use statistics.multimode(), which returns all modes as a list.

Example: Multimodal Data

import statistics# Data (multimodal)data = [1, 2, 2, 3, 3, 4, 5]# Calculate modesmodes = statistics.multimode(data)print("Modes:", modes)

Using NumPy for Mean, Median, and Mode

Alternatively, you can use NumPy for mean and median, and SciPy for mode.

Example: Using NumPy and SciPy

import numpy as npfrom scipy import stats# Datadata = [1, 2, 2, 3, 3, 4, 5]# Calculate mean using NumPymean_value = np.mean(data)# Calculate median using NumPymedian_value = np.median(data)# Calculate mode using SciPymode_value = stats.mode(data)[0][0]print("Mean:", mean_value)print("Median:", median_value)print("Mode:", mode_value)

Summary

• Mean: Average of all values. Use statistics.mean() or numpy.mean().

• Median: Middle value in sorted data. Use statistics.median() or numpy.median().

• Mode: Most frequent value(s). Use statistics.mode() or scipy.stats.mode().

These statistical measures are useful for summarizing a dataset and understanding its central tendency.