What is Histogram: Definition and 68 Discussions

A histogram is an approximate representation of the distribution of numerical data. It was first introduced by Karl Pearson. To construct a histogram, the first step is to "bin" (or "bucket") the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be adjacent and are often (but not required to be) of equal size.If the bins are of equal size, a rectangle is erected over the bin with height proportional to the frequency—the number of cases in each bin. A histogram may also be normalized to display "relative" frequencies. It then shows the proportion of cases that fall into each of several categories, with the sum of the heights equaling 1.
However, bins need not be of equal width; in that case, the erected rectangle is defined to have its area proportional to the frequency of cases in the bin. The vertical axis is then not the frequency but frequency density—the number of cases per unit of the variable on the horizontal axis. Examples of variable bin width are displayed on Census bureau data below.
As the adjacent bins leave no gaps, the rectangles of a histogram touch each other to indicate that the original variable is continuous.Histograms give a rough sense of the density of the underlying distribution of the data, and often for density estimation: estimating the probability density function of the underlying variable. The total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the x-axis are all 1, then a histogram is identical to a relative frequency plot.
A histogram can be thought of as a simplistic kernel density estimation, which uses a kernel to smooth frequencies over the bins. This yields a smoother probability density function, which will in general more accurately reflect distribution of the underlying variable. The density estimate could be plotted as an alternative to the histogram, and is usually drawn as a curve rather than a set of boxes. Histograms are nevertheless preferred in applications, when their statistical properties need to be modeled. The correlated variation of a kernel density estimate is very difficult to describe mathematically, while it is simple for a histogram where each bin varies independently.
An alternative to kernel density estimation is the average shifted histogram,
which is fast to compute and gives a smooth curve estimate of the density without using kernels.
The histogram is one of the seven basic tools of quality control.Histograms are sometimes confused with bar charts. A histogram is used for continuous data, where the bins represent ranges of data, while a bar chart is a plot of categorical variables. Some authors recommend that bar charts have gaps between the rectangles to clarify the distinction.

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  1. S

    Help with Histogram and Boxplot in Python

    I could really use some help here, I am a transfer student so my course load is all out of order. I have a statistics course that requires me to use Python to solve this one question (the 2 parts shown below). I never took any sort of coding before, I don't know where to even start. Can anyone...
  2. Anava1001

    A Normalized differential cross section

    Hello, I know that this question might be a bit silly but I am confused about plotting a normalized differential cross section. Suppose that I have a histogram with the x-axis representing some observable X and the y-axis the number of events per bin. I want the y-axis to show the normalized...
  3. M

    I Uncertainty of histogram bins from MC-simulation

    Hello everyone, I calculated the matrix element of a parton level process and determined the total cross section via a MC-simulation. Then I wanted to look at some differential distributions like the differential cross section with respect to the energy of one of the particles in the final...
  4. Jarvis323

    Optimal Discrete Sampling of Histogram

    I am wondering if this problem has a name, and what is the most efficient way to solve it. Say you have a normalized histogram ##h(P)## (representing a pdf estimated from a large population), with ##n## bins, you want to generate a sample of points ##S## from ##h(P)## of size ##k##, such that...
  5. T

    Is it okay to add error bars into a histogram plot?

    I made a histogram based off a dataset and I calculated the uncertainty of the measurements and I included the error bars into my histogram. Is that okay? I am asking because I never seen error bars included with a histogram. I have included an image of my histogram below:
  6. user366312

    Engineering How can I draw a histogram from Maxwell's distribution using C#?

    I have written the following source code: using System; public class CommonDistributions { public static double Uniform(Random random) { return random.NextDouble(); } static double Gaussian(Random random) { return Math.Sqrt(-2 * Math.Log(Uniform(random))) *...
  7. Vital

    I Reading the vertical data in a frequency histogram polygon

    Hello. Please, take a look at the screenshot from the textbook. They say in the textbook that there are in total 48 data observations, 20 of which lie in the interval 0 - 2, and 6 lie in the interval 2 - 4. Yes, both 20 and 6 are more or less clear on the graph, but how did they come up with 48...
  8. quasarLie

    MATLAB Creating a Histogram with Data from a File.dat in MATLAB

    Hello everyone, I'm trying to make a MATLAB program which read a file.dat and then do a histogram This what I did Data2=importdata('Ma.DAT'); R1=Data2.data(:,17) R1(R1>-9.9) L = 0:0.1:8; histc(R1,L) bar(L,histc(R1,L),'histc') xlabel('R1') ylabel('counts') I want to eliminate all the number...
  9. A

    Appropriate bin size given an energy resolution

    Homework Statement A new particle with the mass of 317 GeV and natural width which is much smaller than the mass resolution of the detector is under investigation. It decays into two photons with equal energies, which are detected in the electromagnetic calorimeter. If one searches the particle...
  10. Z

    MATLAB Coding 2D Signal-Pair Histogram in Python/Matlab

    Hi All, I would like to code the above equation into python (or mathlab) but my number theory skills are not quite up to date. Please, could somebody help me how to start the coding. The equation will be used to calculate 2D signal-pair histograms indicating how often an initial extension e1...
  11. W

    What's the standard deviation of values in the histogram bar

    Homework Statement If one bar of a histogram has been generated with ##n## entries from a total of ##x## measurements, i.e. the event occurs randomly ##n## times in the ##x## event interval, then what is the standard deviation of values in this bar? Let ##k## be the range of values that could...
  12. S

    I What is Weighted Histogram Analysis and How Does it Work?

    I would like to understand the 'weighted histogram analysis method' (wham), which is far to go, but before that am not sure what a weight is? {{Though I understand what is probability density function which has been already discussed on this forum here, and I assume applying weights is a...
  13. F

    I Maximum likelihood w/ histogram, zero probability samples

    I'm trying to replicate a machine learning experiment in a paper.The experiment used several signal generators and "trains" a system to recognize the output from each one. They way this is do is by sampling the output of each generator, and then building histograms from each trial. Later you...
  14. grquanti

    I Logarithmic Binning: Guide & Reference | Physics Forums

    Hello everybody, I have a problem with the logarithmic binning of some data (which are expected to be distributed as a power law). I found this https://www.physicsforums.com/threads/exponential-binning.691834/ What "mute" says is exactly what I need: equally spaced bins on a logscale to...
  15. Sunil Simha

    I Computing uncertainties in histogram bin counts

    I am working on astrophysical data and I have a large number of redshift values of quasars. Now, each redshift estimate comes with its estimated standard error naturally. If I plot a histogram of these redshifts, I would expect the bins counts to also have some sort of uncertainty. I am unable...
  16. J

    Reconstruction of the Fourier transform from its parts

    I am using ROOT to calculate the Fourier transform of a digital signal. I can extract the individual parts of the transform, the magnitude and phase in the form of a 1D histogram. I am attempting to reconstruct the transforms from the phase and magnitude but cannot seem to figure it out. Any...
  17. ChrisVer

    A Normalization vs Reweighting a histogram

    I am trying to clarify what someone means by the words : normalize, reweight. So I'll write what I think they do in practice: 1. Normalization: takes a histogram and scales it by a constant value. The shape of the histogram is not changing, but how the y-axis looks does. 2. Reweight : here I get...
  18. RJLiberator

    Comp Sci C++ (ROOT) Form a matrix and send it to a 2d Histogram

    Homework Statement [/B] 1. I've been tasked with forming a 10 x 10 matrix with elements 0, 1, 2, 3, 4, 5,... and have it display properly. 2. Then, take this matrix and make a 2d-histogram out of it. Homework Equations Here is my code void matrix6( const int n = 10) { float I[n][n]; //...
  19. C

    MHB Frequency-realitive frequency and a histogram frequency

    I am having problems with creating a constructed frequency and realitive frequency distribution and converting it into a frequency chart. This is a list of the past 44 presidents inaguation ages from g. Washington up to barak Obama? 57 61 57 57 58 57 61 54 68 51 49 64 50 48 65 52 56 46 54 49 50...
  20. SSGD

    Time Distribution Histogram for a process with two peaks

    I have been studying a processing time for an industrial process. The present analysis just consists of finding the mean value as if the time was distributed normally. I took a sample of data and made a histogram of the data and realized it is not normally distributed at all. The normal...
  21. T

    Histogram to PDF Conversion: Confirm Experimental Approximation

    Say I have a large data set of 1,000,000 points. If I plot a histogram of this data, I get a bar chart with bins along the x-axis and the number of items in each bin along the y-axis. If I take the number of items in each bin and divide this by the total number of items (1,000,000 in this...
  22. ChrisVer

    What happens when rebinning a histogram with non-divisible number of bins?

    Hi, I am having one histogram that contains 101 bins. I tried rebining it with the TH1::Rebin: histogram->Rebin(2.); But I got the warning message that 2 is not an exact divider of 101. I looked in ROOT TH1 Rebin's page, and read this note: I don't understand what the execution of the...
  23. Rapier

    Root Plotting 2d-Array in Histogram

    Homework Statement The task is to plot a 2-d surface of the potential and field lines calculated from a numerical method. In this case, there is a charged box (v = 1) @ r = 1 (it's not round, but each side is d = 2 and the center of the box is at the origin) and the edges of the box are v=0...
  24. deccard

    Fitting distribution to histogram with low number of counts

    I have one dimensional binned data that has a peak to which I need to fit a distribution, such as Gaussian or Lorentzian, that is described with four parameters, height, width, centroid position and the background. The problem is that the counts per bin are low and the peak is only 5-6 bins wide...
  25. C

    LaTeX How to Create a Histogram in Latex: Step-by-Step Guide

    Homework Statement Hi, I need to create a histogram in Latex. I know how to do this, however, I only know how to do it if I have a limited number of points so I want it so that I can get a computer program to generate a list of numbers and save them to a file and then I can import this to Latex...
  26. L

    MATLAB Plotting a Dose-Volume Histogram from Matrix of Values

    Hi, I have a matrix 150x1 with values between 5.321 to 13.226 and I want to use the matrix and plot a dose-volume histogram (https://en.wikipedia.org/wiki/Dose-volume_histogram). Can someone help me.
  27. J

    Histogram and Rayleigh distribuition

    Homework Statement (iv) Calculatethehistogramforthewaveheightandwaveperiod.(v) Compare the histogram with the Rayleigh distribution.(vi) Calculate exceedance probability distribution for the wave height and wave period using plotting position formulae and compare it with Rayleigh...
  28. K

    Histogram of unequal class width

    for the class 100-199, the f (number of household) is 20, but in the histogram, the frequency is divided by 2 which 20/2 = 10 , but how can it show that in the class 100-199 , the total frequency of 100-199 is 10 ? when i look at the histogram, i would directly think that there are f=10 in the...
  29. Ackbach

    MHB PGFPLOTS Histogram: Customizing X-Axis Labels

    Warning: requires the tikz and pgfplots packages. I've got my histogram almost where I want it: \begin{center} \begin{tikzpicture} \begin{axis}[ tiny, width=6in, ymin=0, ybar interval, ] \addplot+[hist={bins=10,density}] table[row sep=\\,y index=0] { data \\ 565 \\...
  30. D

    Histogram with # on edge of bin?

    let's say I have 10 data points. And one of my data points is 270. Then let's say two of my bins are 260-270 and 270-280. Which bin would you put the 270 in? Or would such a choice of bin range be inappropriate and new ranges have to be chosen?
  31. P

    MATLAB Histogram coloured by different hues in matlab

    Dear Physics fans, Are we all okay? I hope so. I was wondering if you could help me please? I am banging my head against a wall in MATLAB and I think what I need to do should be very easy. I have a histogram of intensities and I could like to colour then starting off at black and...
  32. C

    Histogram Bin Sizing Methodology

    Hey all I have what I assume to be a fairly vague question. I'm taking a programming class right now for MATLAB and the current project we are working on is a simple histogram display from reading an excel data file. The coding is extremely easy however, having never taken a statistics course...
  33. F

    Python, matplotlib plot 2D histogram on polar axis.

    Any python/matplotlib experts out there?? This one has been driving me crazy all day. I have three vectors, azimuth, frequency and power, which I would like to histogram and plot on a polar axis. I can plot a scatter plot this way no problem but the histogram gets messed up somehow. An example...
  34. O

    Entropy of a histogram with different bin sizes

    I'm wondering if there's an expression/correction for finding the entropy of a density using histograms of different bin sizes. I know that as the number of bins increases, entropy will also increase (given a sufficient number of data points), but is there an expression relating the two? All I...
  35. C

    How to get the CDF from a histogram

    Hello, I have a histogram, where I count the number of occurrences that a function takes particular values in the range 0.8 and 2.2. I would like to get the cumulative distribution function for the set of values. Is it correct to just count the total number of occurrences until each...
  36. Z

    Calculating Standard Error of Mean for 2D Histogram Data

    Hey everyone, I'm not sure if there is an effective answer to my problem, but here goes: I am working on Ramachandran plots for short peptides (3 amino acids long). For every snapshot of the protein (this would be my data point) there are two angles being recorded, the phi and psi angles...
  37. N

    Mathematica Mathematica: Extracting histogram information

    Hi I have a histogram of some numbers following a PDF, such as Histogram[RandomReal[1, 100]] What I want is to extract the information contained in this histogram in a list, i.e. get a list of the bin value (e.g. the average value it represents) and the number of entries in it. Is using...
  38. manjuvenamma

    Draw Histogram in Excel: Is it Possible?

    Is it possible to draw histograms in Microsoft Excel? I see all charts of icons in the Excel tool bar but no histogram.
  39. M

    How to read Z-score histogram for variability?

    Hi All Would be most grateful if there are some pointers given on this question. Ques: There is a range of different brands of museli bars with information of nutritional values. E.g Museli bars A with variables of Vitamin, Fat, Potassium values and so on. I have been asked to plot a...
  40. D

    Obtaining a normalized PDF from a histogram?

    Suppose I have a regular histogram, I can normalize it by dividing the frequency counts by the total number of counts (at least I believe that's all you need to do). What you're left with should be an approximation to the underlying PDF (probability density function). What I'm asking is how...
  41. T

    Confused on creating a normalized histogram (on excel)

    I have all the information I need, but I just need a bit of help on getting my data on a normalized histogram in excel. First, if I'm not mistaking, a normalized histogram is just a normal histogram where it is roughly symmetrical about the curves centerline, is that correct? I have a list...
  42. S

    How to create a histogram of a nifti file

    Hi, I'm trying to create a histogram of a .nii file but it's now working. 1. loading the nifti file: >> Try2=load_nifti('DM.nii'); 2. hist(Try2); that generarates a histogram, where most of the values are concentrated between -150 and 200.(3 bars,the middle one is between -50 and 100). 3...
  43. R

    Quantitive Histogram Comparison

    I have two histograms that I would like to compare quantitatively. The values of the first histogram have respective relative errors for each bin. The second histogram has no statistical uncertainty. I could compute probabilities for each bin that the exact values would fall into a given...
  44. matt_crouch

    Matlab code fitting a line to a histogram

    Im analyzing some data from a previous student I am trying to plot a line of best fit over the histogram and hense find the value of the coefficiants the files had to be loaded as -ascii so this is the code i have typed so far x=load('filename.mat','-ascii'); mean(x); hist(x,300) this...
  45. matt_crouch

    Plotting a best fit curve over a histogram

    Im analyzing some data from a previous student I am trying to plot a line of best fit over the histogram and hense find the value of the coefficiants the files had to be loaded as -ascii so this is the code i have typed so far x=load('filename.mat','-ascii'); mean(x); hist(x,300) this then...
  46. C

    Expected Value of Distribution on Histogram: T/F

    Homework Statement 4: (T/F) The expected value of a distribution always occurs at the center of the tallest bar on the histogram. Homework Equations (no equation necessary for it is T/F) The Attempt at a Solution I believe this is false for the expected value can be definite or...
  47. A

    How can I determine if a set of numbers is truly random based on a histogram?

    [b]1. The problem statement If i generate a list of 300 random numbers in excel, each number between 1-50 for example, and i plot the frequency that each number comes in a histogram, how can i tell, looking at the histogram, if the numbers are really random? is there a certain distribution...
  48. L

    What is the second equality in the bias of histogram estimate derived from?

    Suppose we wish to estimate a probability density given the points {x_1, ..., x_n} using a histogram \hat{f}(x). I have a book that says Bias(\hat{f}(x))=E_f(\hat{f}(x))-f(x)=\frac{1}{2}f'(x)(h-2(x-b_j))+O(h^2) for x\in(b_j,b_{j+1}]. Can someone explain where the second equality comes from? I...
  49. H

    Addressing Odd Behaviour in Histogram Bin Counting for Experimental Data

    I am making a histogram for some experimental data in OpenOffice Calc (Excel equivalent). However, when I have it count frequency for a certain number, it displays odd behaviour. For example: Data: 1 499500 1000 375250 1000 Bins: 0 50000 100000 150000 200000 The problem is...
  50. M

    Creating Histogram & PDF for Data Sample

    Hi All, I just need your small help in Matlab programming of histogram and PDF Task to create and reproduce histogram and Probability distribution function for a given data sample (Inter packet arrival times).please see the attachment for the data (TV_80_port_testing.dat) and...