# Histograms

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### 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.

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.

Skill Path

Intermediate

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