Histogram Definition and 68 Threads

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. mcknia07

    How to Make a Histogram: Stats Homework Help

    I am trying to help my brother on his Stats homework, but for the life of me, I can't rememeber how to make a histogram. He has the answers to compare to, but is unsure how they got to them, as am I. It's been so long since I have done this stuff, I need a little refresher. Google is not helping...
  2. S

    Mathematica Changing interval in Histogram, Mathematica

    Hello again. Sorry for all the posts. I have a histogram of frequencies in Mathematica and the intervals on the x-axis are predefined and kind of unrepresentative. I changed the bin number (with 'Histogram[mydata, binnumber]') but I can't seem to find anything on the internet about changing...
  3. B

    Histogram of number of units selected

    I have some things that have a 7% chance of being blue, 10 of these things are put in a box. What is the percent chance that the box will have exactly one blue thing? Two blue things? and so on.. I have simulated this and came up with the following (all appx) 0 - 37% 1 - 37% 2 - 18% 3 -...
  4. S

    Mathematica Simulating Normal Distribution in Mathematica: Histogram and PDF Plotting

    Hi guys, On my homework, I'm simulating a normal distribution on Mathematica by adding up a bunch of RandomReal[] , that is, uniform(0,1) random variables, and using the central limit theorem. I would like to plot both the histogram and the actual Gaussian probability density function on the...
  5. A

    Histogram fitting: fit parameter errors not corresponding with optimizer results

    Hi I'm having some big problems with some data! I will try to keep this as simple as possible... I have a random variable that admits a probability distribution that I have a fit function for. With a large enough number of samples I can get good estimates of the fit function parameters via...
  6. P

    Graph analysis - how closely histogram fits poisson curve

    Homework Statement Its about random radioactive decay. I have a histogram showing the number of counts recorded in 3 second intervals and I've drawn the Poisson Curve on the same graph. I have a graph for 50 intervals and one for 100 intervals and I need to analyse how well the data...
  7. P

    Graph analysis - how closely histogram fits poisson curve

    Homework Statement This isn't really a question, its a report thing. Its about random radioactive decay. I have a histogram showing the number of counts recorded in 3 second intervals and I've drawn the Poisson Curve on the same graph. I have a graph for 50 intervals and one for...
  8. Saladsamurai

    Excel Histogram How does it calculate bin width

    Hey people, I am trying to write my own histogram making code since the Excel one sucks IMO. I am having some trouble thinking the whole bin 'width' thing through though. I plan on using the formula number of bins = k = 1.87(N - 1)0.40 + 1 Then I was going to figure out the bin...
  9. M

    Force Measurement Histogram: Vertical vs. Horizontal Axis

    I am a little confused about a histogram of force measurements. I was asked for my physics lab to state what the vertical axis and horizontal axis represent for a histogram of force measurements? the physics lab consists of pulling a wooden block with a force sensor to record the tension...
  10. P

    What's the point of a histogram of baseline measurments?

    Hey folks, I am trying to write a paper and my suprevisor told me to make baseline measurments of the two groups and plot a histogram for each group and include that in my results. Problem is, I don't know that purpose of this histogram is and I don't know what to write. I mean yeah histogram...
  11. A

    What is a Histogram? - Answers & Explanations

    Can you please tell me what a histogram is? Some definitions seem to allow any bar chart where the areas of the bars are proportional to the frquency, which would allow underlying discrete distributions, such as he number of people expressing preferences for different makes of car, where the...
  12. A

    Simple Histogram using Mathematica - please

    Hi. I am new to using Mathematica v7 and would like to know how to generate a very simple histogram. The data is: data = {1.5, 2, 0, 0.5, 1, 2, 1.5, 3, 0, 0.5, 1, 2, 2, 3, 3.5, 0, 1, 4, 2, 0.5, 1, 0, 2, 1.5, 0, 1.5} I can generate the histogram using Histogram[data] but how do I set...
  13. E

    Experimental physics histogram problem

    Homework Statement You have run an experiment and generated a histogram. Suppose you had 853 counts in the bin centered at 1.60, and 2,439 counts in the bin centered at 1.85. If you were to repeat this experiment (by measuring the same source for the same time period, delta t) you know...
  14. N

    Understanding Molecular Speed: Finding v avg and v-rms Using a Histogram

    Hello! I have a question. When I am provided with a histogram, with % of molecules along the y-axis and speed range (m/s) along the x-axis, how do I use this to determine the average speed (v avg) and v-rms (root mean square) of the molecules in the gas? I am very puzzled. Any suggestions or...
  15. P

    Probability Histogram and Central Limit Theorem

    Hi, I have trouble understanding the convergence of empirical histogram to probability histogram and the convergence of empirical histogram to normal curve. It was written in my lecture notes that as the number of repetitions goes large, empirical histogram converges to probability...
  16. A

    Creating a histogram and then applying a gaussian fit. Help

    Ok, I need to take the data: D1 D2 6.5 3 6 4 6.7 5.5 7 3.8 6.3 4.5 8.6 5.8 5.5 4 7 3.5 7 4.5 7 5 6.5 4 6.8 3.2 7 3.6 6 4.5 6 2.8 and make a histogram (centered around 0 -- i.e. 0 will not be an edge of a bin) of the data...
  17. Saladsamurai

    How do I determine the class size for creating a histogram in statistics?

    I have a quick question regarding a stats problem in my girlfriend's text. It is pretty easy I suppose, but I am not quite sure; the text does not appear to give a "general form" of how to obtain the info. Feel free to correct me if I misuse words here, I am not familiar with the stats lingo...
  18. X

    Histogram of Sinusoid: Is it the Same as PDF?

    I am looking at values of a sinusoid, y = A sin(2*Pi*f*t), oscillating between A and -A at a frequency of 25 Hz over 0.650 milliseconds. If I find the histogram of the sinusoid, is this the same thing as the probability density function of that sinusoid? If this is not the case, what does...
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