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.

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.

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)

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.

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.

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.

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.

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.

Bimodal Dataset

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

Multimodal Dataset

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

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.

Peak of Unimodal Distribution

The center of a dataset is the peak of a unimodal distribution. The statistics that describe the center of a dataset are the mean and median.

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.

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.

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