Distributions

Matplotlib Function To Create Histogram

In Python, the pyplot.hist() function in the Matplotlib pyplot library can be used to plot a histogram. The function accepts a NumPy array, the range of the dataset, and the number of bins as input.

import numpy as np
from matplotlib import pyplot as plt

# numpy array 
data_array = np.array([1,1,1,1,1,2,3,3,3,4,4,5,5,6,7])

# plot histogram
plt.hist(data_array, range = (1,7), bins = 7)

Mean of a Dataset

The mean, or average, of a dataset is calculated by adding all the values in the dataset and then dividing by the number of values in the set.

For example, for the dataset [1,2,3], the mean is 1+2+3 / 3 = 2.

Histogram Bins

In a histogram, the range of the data is divided into sub-ranges represented by bins. The width of the bin is calculated by dividing the range of the dataset by the number of bins, giving each bin in a histogram the same width.

What is a Histogram?

A Histogram is a plot that displays the spread, or distribution of a dataset. In a histogram, the data is split into intervals, called bins. Each bin shows the number of data points that are contained within that bin.

Histogram Bin Count

In a histogram, the bin count is the number of data points that fall within the bin’s range.

Histogram’s X and Y Axis

A histogram is a graphical representation of the distribution of numerical data. In a histogram, the bin ranges are on the x-axis and the counts are on the y-axis.

An example histogram.

The title of the histogram is 'Exercise Class Age Distribution'.

Along the x-axis, labeled 'Ages', the bin ranges are each 10 years, starting with age 20 and ending at age 70. The 5 bin ranges are as follows: 20-30, 30-40, 40-50, 50-60, and 60-70.

Along the y-axis, labeled 'Count', the values are whole numbers. The values start at 0 and end at 7.

The first bin range, ages 20-30, has a count of 7. The second bin range, ages 30-40, and the third bin range, ages 40-50, each have a count of 4. The fourth bin range, ages 50-60, has a count of 3. The last bin range, ages 60-70, has a count of 2.

Each bin range is the shape of a rectangle starting at count 0 and ending at the bin ranges' respective count. These rectangles are all the same color blue with a black outline. Also, there is no white space between the bin ranges.

Unimodal Distribution

Modality describes the number of peaks in a dataset. A unimodal distribution in a histogram means there is one distinct peak indicating the most frequent value in a histogram.

Left-Skewed Dataset

A left-skewed dataset has a long left tail with one prominent peak to the right. The median of this dataset is greater than the mean of this dataset.

Multimodal Dataset

If a histogram has more than two peaks, then the dataset is referred to as multimodal.

Bimodal Dataset

A bimodal dataset has two distinct peaks. This typically happens when the dataset contains two different populations.

Uniform Dataset

A uniform dataset does not have any distinct peaks.

As seen in the histogram below, uniform datasets have approximately the same number of values in each group represented by a bar - there is no obvious clustering.

An example of a uniform dataset.

There is a histogram shown labeled 'Uniform Distribution'. Each of the many bars on the histogram are about the same width and are also similar in height.

Right-skewed Dataset

In a histogram, if the prominent peak lies to the left with the tail extending to the right, then it is called a right-skewed dataset. In this case, the median is less than the mean of the dataset.

Symmetric Distribution in Histogram

In a histogram, the distribution of the data is symmetric if it has one prominent peak and equal tails to the left and the right. The Median and the Mean of a symmetric dataset are similar.

An example of symmetric distribution in a histogram. The example is titled 'Symmetric'.

The example is a histogram without labels or units. It also has a key in the upper right for the mean, indicated by a dark blue line, and median, indicated by a green line. The histogram is light blue with one peak and equal tails to the left and right of the peak. From left to right: there is a dark blue line (mean) and green line (median) next to each other at the center of the histogram's peak.

Dataset Outliers

An outlier is a data point that differs significantly from the rest of the values in a dataset.

For example, in the dataset [1, 2, 3, 4, 100] the value 100 is an outlier because it lies a large distance from the rest of the data.

Spread of a Dataset

The spread of a dataset is the dispersion from the dataset’s center. The descriptive statistics that describe the spread are range, variance and standard deviation.

For example, for the dataset [1, 4, 7, 10], the range of the dataset would be the maximum value of the set - the minimum value of the set, or 10 - 1 = 9.