Equal width binning disadvantages. His results are summarized in Figure 1. IntervalIndex : Defines the exact bins to be used. The width of intervals is: w = (max-min)/k Equal Width Binning Description. Jan 20, 2020 · There is no guarantee about the distribution of items in each bin. The NumPy library's histogram function can be used to implement equal-width binning. This has a smoothing effect on the input data and can also Feb 4, 2019 · 23. x = np. 1% on each side to include the minimum and maximum values of x. 01 ppm the most common choices). Por exemplo, você pode criar um quadro de dados de exemplo e atribuir a coluna idade a 5 compartimentos com pd. Equal Width Binning: This algorithm divides the continuous variable into several categories having bins or range of the Unsupervised binning methods transform numerical variables into categorical counterparts but do not use the target (class) information. Aug 17, 2023 · The most common ones include equal-width binning, equal-frequency binning, and k-means clustering. 2 values fall into the 6-10 bin. k Skewed data cannot be handled well by Equal-width Binning This method – without complexity in implementation and with utility for evenly distributed data – splits the range of our dataset into intervals that are of identical size. cut_number(): Makes n groups with (approximately) equal numbers of observation; cut_interval(): Makes n groups with equal range; cut_width(): Makes groups of width; My go-to is cut_number() because this uses evenly spaced quantiles for binning Equal-width binning and equal-size binning These two approaches are straightforward approaches for binning (Thomas, Crook, & Edelman, 2017a). There are different methods of binning: There are several methods of binning that can be used, including equal width binning, equal frequency binning, and k-means binning. For example, dividing a range of values from 0 to 100 into 10 Jan 1, 2012 · Equal width partitioning divides the total interface variability equally between bins, while equal probability partitioning ensures that each bin has equal populations of components [5]. A practical example would be choosing five bins within a 0-100 data range, where each bin covers an interval precisely measuring 20 units (0-20, 21 Analyzing this data is difficult. The MAB scheme used a maximum of 44 bins while the manual binning scheme used a maximum of 294 bins that were evenly spaced between an RMSD of 0 and 20 Å and end-to-end distance of 0–26 Å. qcut(df['SepalLengthCm'], 4) Oct 26, 2017 · What are the different methods of binning? There are several methods of binning, including equal width binning, equal frequency binning, and quantile binning. References: Step 4: Select Analysis ToolPak and press OK. Select Histogram and press OK. Equal-sized bins allow you to gain easy insight into the distribution, while grouping data into custom bins can allow you to gain Oct 12, 2023 · Equal-width binning ensures that each bin has the same range of values, which helps to maintain the balance and equal representation of the data in each bin 22. Charge from adjacent pixels in CCD image sensors and some other image sensors can be combined during readout, increasing the line rate or frame rate. Works quite well despite simplicity. Data points Apr 13, 2022 · Real-world data tend to be noisy. The range of x is extended by . It is a straightforward method but may not work well if the data distribution is skewed or has outliers. For equal-width binning, the user firstly decide the number of bins, then the whole range of predictor values is divided into a pre-specified number of equal-width intervals. In general, we should not bin, because binning will lose information. Matching Feb 2, 2021 · A total simulation time of 2. To obtain a good bin, several conditions must be met: (1) empty data are separated into its own bin, (2) each bin has at least 5% of the total data, and (3) no bin has zeros for either good or bad Pixel binning. The intervals can be of equal or unequal size, and can be defined using different methods, such as: Fixed Width Binning: Dividing the data into a fixed number of equally sized bins. pyplot as plt. Each method has its own advantages and disadvantages, and the choice of method will depend on the specific requirements of the analysis. May 22, 2024 · Understanding Decision Trees. Oct 31, 2023 · Data discretization can be carried out using various methods, each with its advantages and disadvantages: 1. Image Data Processing. 25 V for the NCA, LFP 1, and LFP 2 cells, respectively. How can binning affect the results of data analysis? For sake of completion here are the 3 methods of converting continuous to categorical (binning). Another way to adjust the bin size is by specifying the bin boundaries. bin1: 5,10,11,13,15,35,50,55,72 I. It depends on what model we are Feb 12, 2018 · Equal size binning: Spectrum is divided in simple rectangular regions of the same size. Issues with binning using pandas. A key step in this process is the quantification of spectral features, which is commonly accomplished by dividing an NMR spectrum into several hundred integral regions or bins. Thus, i th interval range will be [A + (i-1)w, A + iw] where i = 1, 2, 3…. Para usar binning em Python, você pode empregar a biblioteca pandas para executar binning de largura e frequência iguais em uma coluna numérica. If None, output dtype is consistent with input dtype. The range of numerical values is partitioned into segments of equal size. 2. 10% of the data in each of 10 bins) Equal Quantitative Ranges (intervals of equal width, e. Peaks can be splitted across multiple bins Improving accuracy of students’ final grade prediction model using optimal equal width binning and synthetic minority over-sampling technique December 2015 Decision Analytics 2(1) Nov 28, 2023 · Introduction Data binning is a powerful technique in data analysis, allowing us to organize and gain insights from datasets effectively. If we have a "high bias" model, binning may not be bad, but if we have a "high variance" model, we should avoid binning. Equal width binning divides the range of values into a specified number of equal-sized intervals. Self-Guided via CART Available only for continuous variables, the discretization is accomplished via CART to determine the Mar 12, 2015 · In this research, we present how data can be preprocessed using a discretization method called the Optimal Equal Width Binning and an over-sampling technique known as the Synthetic Minority Over-Sampling (SMOTE) to improve the accuracy of the students’ final grade prediction model for a particular course. Binning is the process of dividing a range of numerical values into smaller sub-ranges called bins or intervals. Home; Guides An object of class rbin_equal_length. Equal-width binning is often used to produce histograms—a bar chart that shows the frequency of each bucket. The original data values ‚Äã‚Äãare divided into small ranges known as bins and then replaced by an overall calculated value for that bin. Fixed-Width Binning 2. Creating a Shorter Version of the Frequency Table To create a shorter version of the frequency table with fewer intervals, we can use a variety of methods, such as equal width or equal frequency binning. In this exploration, we’ll dissect a Python script that utilizes NumPy and Pandas to implement two types of data binning: equal-width and equal-depth. These methods will allow you to bin data into custom-sized bins and equally-sized bins, respectively. The simplest example of using binning is to create a histogram of a variable. qcut() for binning your data. Bin continuous data using the equal length binning method. For example, here i am selecting the Cell Number A1 to A13 as an input range and cell number C4:C5 as bin range. Consider the following dataset (sorted in non-decreasing order): <13, 38, 41, 44, 45, 81, 85, 88, 90, 96, 103, 125, 130, 137, 152> (1) Perform the equal width binning on the above data with 3 bins using the method we discussed in the class. Consider (e. Feb 18, 2023 · There are two primary types of binning methods: frequency binning and equal width binning. In this Sep 4, 2010 · This function is finding how many bin-widths above the minimum your value is, by dividing (value - minimum) by the bin width. cut() and . Most of the binning strategies pro posed in the literature for selective assembly involve one of two heuristic methods: equal width or equal area partitioning schemes. to_df() equal width bins can easily be created using the cut function from pandas. 0]). On python, you would want to import the following for discretization: from sklearn. 1- Equal Width Binning: The algorithm divides the data into k intervals of equal size. Sep 30, 2022 · The whole idea behind pixel binning is that it allows putting more but smaller pixels instead of fewer but larger pixels on a camera sensor. Unlike equal-height binning, where all buckets have roughly the same frequency, in equal-width binning, each bucket can have a different frequency. Fixed-Width Binning We manually create fix width bins based on some rules and domain knowledge. Arules Package: Discretize a continuous vector into a discrete vector with specific categories to produce a table of Jul 6, 2020 · In a twitter thread, I referred to the analysis in Axtell (2001) as an example of research where data binning might not be warranted and could have influenced the analysis. In equal width binning, data is divided into intervals of equal width. The width of the intervals is defined as (max - min) / N. For example, if the range of the variable is 0–20 and we want 5 bins, then each bin will cover a range of 4 units (0–4,4–8,8–12,12–16,16–20). Equal-width binning divides the range of data values into bins of equal width. For equal width bins let’s say you divide the data into 25, 1000 unit bins – now you can simplify your data analysis and set monitors in production. The bias arises because these methods establish a set of bins in which the smallest data value is at the extreme left of the lowest bin and the largest data value is at the extreme right of the highest bin. The discretized values are usually one-hot Description. qcut method for bins with equal number of elements. This operator discretizes the selected numerical attributes to nominal attributes. The number of bins parameter is used to specify the required number of bins. mquantiles again until sample sizes are equal or only one bin exists. I’ve selected 2 numerical variables to work with: As we can see, the code above creates a histogram with six equal-width bins that span the range from 0 to 20. Axtell (2001) condenses 5,541,918 observations from U. So if there are n number of bins, then each bin will have equal width, and the range of each bin is defined as [m i n + w] [min + w] [m i n + w], [m i n + 2 w] [min Binning in Statistics: Understanding Equal-Width and Equal-Frequency Binning Techniques Statistics often involve organizing and analyzing large data sets, and one way to do this is through binning. Custom Binning. The bin width is thus the smallest possible that could be used to stuff these data into a desired number of bins. Then, if the values of the variable vary between 0 and 100, the bins can be 0–20, 20–40, 40–60, 80–100. Based on the minimum width requirement, voltage ranges under equal-width binning and equal-capacity binning are summarized in Table 3. Dec 27, 2021 · In this tutorial, you’ll learn about two different Pandas methods, . com/playlist?list=PLnZQydCjRQJyczqWhWmqlvPOg8WSWJ8rjData S videtherangeofk intervalssimultaneously(i. Although associated with loss of information, this aggregation reduces the amount of data to Jun 12, 2023 · Equal Width Binning. rbin 0. Equal-width binning divides the range of the data into N intervals of equal size. Incremental methods begin with a simple discretization and pass through an improvement process, needing an additional criterion to know when to stop discretizing (Cerquides and Mantaras, 1997). Adaptive Binning Lets discuss them one by one: 1. There are binning strategies such as equal width binning or equal frequency binning. Equal width schemes, as the name suggests, partition the dimensional distributions of the components so that the bins have equal widths (see Pugh 1986; Thesen and Jantayavichit Sep 2, 2023 · Binning can be applied in different ways such as equal width, equal frequency, or using clustering algorithms. We only care about how many full bin-widths fit into the value, not fractional ones, so we use ROUNDDOWN to chop off all the fractional bin-widths (that is, show 0 decimal places). Disadvantages of Binning [Original Blog] When it comes to data analysis , binning is a method used to smooth out data by grouping it into intervals or "bins". Some question sets might have more than one correct solution, while others might not have a correct solution. This function will automatically assign data points to bins based on their Nov 28, 2023 · It is really helpful in working with skewed data distribution as the data in each bin is equal. This technique is useful in summarizing and visualizing large data […] Jan 29, 2021 · Equal-frequency binning divides the data set into bins that all have the same number of samples. Data cleaning (or data cleansing) routines attempt to smooth out noise while identifying outliers in the data. show() Here bin_pos is a list representing the positions of the boundaries of the bins (see related question here. 8976,900. firms into 13 data points to provide evidence in favor of Zipf’s law. $500) The analyst needs to decide only on the number of intervals to be created. Therefore. Jan 6, 2024 · Here are three common types of data binning algorithms: Equal Width Binning. This method is useful for data with a normal distribution. A flexible and comprehensible machine learning approach for classification and regression applications is the decision tree. Binning is actually increasing the degree of freedom of the model, so, it is possible to cause over-fitting after binning. Equal frequency binning divides the data into bins containing an equal number of data points. df['Sepallength_quartle'] = pd. This gives us more control over the bin sizes and allows us to define bins of irregular widths. A histogram divides the range of the data by using k evenly spaced cutpoints. n_bins number of clusters are made which divides the dataset into n_bins number of bins(or clusters). 8976], (795. The qcut function is slightly different. Computer Science questions and answers. Method 2: Specify Bin Boundaries. Feb 21, 2023 · Binning is the process of dividing a continuous variable into a set of discrete intervals or bins. 0. If its this simply, use Maths node to add another column using Math Expression RowIndex. Jan 1, 1995 · The number of bins, k, in the equal width interval discretization was set to both k -- 10 and k -- m a x { l , 2 · log^}, where / is the number of distinct observed values for each attribute. Sep 2, 2021 · What is Feature Binning? Feature binning refers to a technique to transform or bucket the numerical or continuous feature into a categorical variable. Jun 6, 2016 · Here is a MWE to display a histogram with normally distributed sample data: import matplotlib. Apr 5, 2021 · In this post, we’ll walk through three different methods for binning numerical features with specific examples using NumPy and Pandas. Uniform Binning. Binning attempts to minimize effects Apr 20, 2011 · Equal frequency and equal width binning in R. Only np. $\endgroup$ – Dec 28, 2020 · Binning would be wise to apply if your continuous variable is noisy, meaning the values for your variable were not recorded very accurately. 5. matplotlib. The conclusion, such as a class label for classification or a numerical value for regression, is represented by each leaf node in the tree-like structure that is constructed, with each internal node representing a judgment or test on a feature. However, to consider Jan 12, 2023 · Partitioning in Data Mining | Equal Width Equal | Frequency | Clustering Partitioning Mahesh HuddarThe following concepts are discussed:_____ 1. This algorithm divides the continuous variable into several categories having bins or ranges of the same width. Aug 7, 2019 · The simplest binning technique is to form equal-width bins, which is also known as bucket binning. 9, 1. Set up the Equal-Width Discretizer in the following way: Jul 4, 2022 · Equal–width discretization. df: A data. 5 to 6 feet. cut() para binning de largura igual e pd. The trick is that width is not just width, it is width of each interval. float64 are supported. 2. For each bin, show the bin interval, data values in the bin, and Mar 18, 2022 · Binning by frequency, these common ages will be better separated and more beneficial to the model. 02, 0. If samples are not equal between bins, the code reduces the number of equally-spaced quantiles by 1 and calls stats. Using weather data extracted from the database using the open-source package RasgoQL, dataset = rql. K means: Here kmeans clustering is used to determine bin’s width. T h e heuristic was chosen based on examining S-plus's histogram binning algorithm (Spector 1994). Quantile binning assigns the same number of observations to each bin. 0 μs was generated for each binning scheme (338 and 200 WE iterations for the MAB and manual binning schemes, respectively). Mar 2, 2020 · Pandas: divide column into three bins of exact same size. Each segment represents a bin. 04, 0. Equal-width binning divides values into ranges of equal width. A less commonly used form of binning is known as equal-frequency binning, in which we divide a dataset into k bins that all have an equal number of frequencies. sequence of scalars : Defines the bin edges allowing for non-uniform width. It is a slight exaggeration to say that binning should be avoided at all costs, but it is certainly the case that binning introduces bin choices that introduce some arbitrariness to the analysis. No extension of the range of x is done. 004,795. Note: This question is part of a series of questions that present the same scenario. I hard coded the tolerance in the example, but this could be modified to a keyword argument if desired. Then, the cut () function can be used to divide the data into desired number of bins, with the parameter “q” specifying the number of bins. mstats. Each method has its own advantages and disadvantages, and the best approach may vary depending on the data and the desired outcome. Using binning technique, we can convert all the values in this variable into ranges. Noisy data is data with a large amount of additional meaningless information in it called noise. frame with independent variables and target Mar 21, 2022 · Choose A2:A16 as the Input Range, C2:C7 as the Bin Range, E2 as the Output Range, and check the box next to Chart Output. This is particularly important when Aug 23, 2023 · Equal-Width Binning. It divides the range into N intervals of equal size. In fact, you can define bins in such a way that no items are included in a bin or nearly all items are in a single bin. This tutorial explains how to perform equal frequency binning Mar 15, 2023 · Example of Data Discretization. 25V, and 0. Step 5: Now select all the data cell and then select ‘Data Analysis’. Dec 9, 2019 · In general, however, equal width is better for graphical representations (histograms) and is more intuitive, but it might have problems if the data is not evenly distributed, it's sparse, or has outliers, as you will have many empty, useless bins. Unfortunately, I could not find a clear answer. For example, if ages in a dataset range from 18 to 80, equal width binning with a bin width of 10 would create the following age groups: 18-28, 29-39, 40-50 Apr 27, 2022 · How to apply equal width binning in data miningData Science Questions and Answers :https://youtube. Jul 5, 2023 · In general, the bins must be adjacent with an equal size, but sometimes unequal bin sizes are necessary for processing the statistical data of a variate 22,23,24. cut method for arbitrary binning which I use for equal wdith bins and pd. Equal Width Binning. Each method has its own advantages and disadvantages depending on the nature of the data. We would like to show you a description here but the site won’t allow us. randn(100) plt. Mar 15, 2024 · The size and number of intervals can be adjusted to provide the most meaningful representation of the data. In comparison, a superpixel of the same size carrying the photonic data of multiple smaller pixels has to guess Aug 28, 2020 · A quantile discretization transform will attempt to split the observations for each input variable into k groups, where the number of observations assigned to each group is approximately equal. 2V, 0. Nov 25, 2010 · The interpretation of nuclear magnetic resonance (NMR) experimental results for metabolomics studies requires intensive signal processing and multivariate data analysis techniques. The interval width is simply the range [A, B] of the variable divided by k, w = (B-A) / k. , 10 bins \([0, 0. print_plot. There are three data smoothing techniques as follows - Binning : Binning methods smooth a sorted data value Oct 3, 2017 · To get this you drag-and-drop the 'Retrieve gaussian' dataset from the left pane near the top, and the 'Discretize' from the lower left pane. all values between 5 and 75 bin2: 92 I. 1. Oct 23, 2023 · 3. We can carry out equal-frequency discretization in Python using the open source library Feb 4, 2017 · Given a dataset, I want to partition it into 4 bins using both equal frequency binning and equal width binning as described here, But I want to use R language. all values between 75 and 145 bin3: 204,215 I. Feb 16, 2023 · Unsupervised discretization is a crucial step in many knowledge discovery tasks. Jan 20, 2020 · Exam DP-100 topic 2 question 43 discussion. 0. Different bin sizes can reveal Aug 5, 2019 · This usually indicates that equal-length binning will result in bins in the tail of the distribution that have only a few observations. Apr 13, 2017 · However, by definition, a histogram displays frequencies by means of areas. However, in order to calculate model drift, you need to make sure the bins in Overview. I set 'size of bins' for 'Discretize' and connected two components with each other and the 'res' which For an example of the different strategies see: Demonstrating the different strategies of KBinsDiscretizer. ) the data {0,1,2,4,8,16,32,64}, to be shown in the range [0,100] with two bins. In this strategy each bin will have equal frequency of data points. Equal-width Binning. If we put it at 6, the height of the left bar multiplied by (6-0) = 6 equals 4, whence the height is 4/6. To make this data easier to work with, we can discretize it into the following categories: 4 to 4. For instance, if you’re categorizing ages, you might choose bins like 0-10, 11-20, 21-30, and so on. float32 and np. Binning in pandas. Mar 1, 2023 · Taking the mean and standard deviations of a set of H under different widths, the minimum width is determined as 0. Equal-width discretization consists of dividing the range of continuous values into k equally sized intervals. Use PROC HPBIN to bin data into equal-length bins. The performance of estimators of τ2 (measured by bias and coverage) affects their usefulness Dec 1, 2011 · By interval width, do you just mean first 100 rows in one bin, next 100 rows in bin two etc. This method involves dividing a continuous variable into a specified number of bins of equal width. Jul 7, 2020 · The most common form of binning is known as equal-width binning, in which we divide a dataset into k bins of equal width. Then click OK. Then, binning could reduce this noise. Pixel binning, often called binning, is the process of combining adjacent pixels throughout an image, by summing or averaging their values, during or after readout. Mar 28, 2015 · It also seems incomplete by not discussing the disadvantages of binning. The width of each bin is (Max – Min) / k. dataset('Table Name') df = dataset. This discretization is performed by simple binning. Types of Binning There are two types of binning techniques: 1. What is the difference between both methods? It seems to me that both do the same and it is just a matter of terminology. Pandas come up with a pd. This can be useful when you want to divide data into uniform intervals, regardless of the data distribution. 5 to 5. S. float32, np. In Apr 16, 2024 · To implement equal frequency binning in Python, one can use the pandas library to first sort the data in ascending order. The heights are continuous data and can range from 4 feet to 6 feet. discretisers import EqualWidthDiscretiser. 342]]). Variable bins for each row in pandas dataframe. 5 feet. Equal frequency: each bin contains the same number of data points. Equal frequency will instead guarantee that every bin contains the roughly the same amount of data Apr 14, 2022 · Equal width (or distance) binning : The simplest binning approach is to partition the range of the variable into k equal-width intervals. ,equal-widthandequal-frequency),needing an additional input from the user to determine the number of intervals. float64}, default=None. Sep 23, 2019 · 4. I would recommend avoiding equal width binning when your continuous variable is . 9000. If a variable has the range [Min, Max] and you want to split the data into k equal-width bins (or buckets), each bin will have width (Max - Min) / k . dtype{np. For example, if you’re discretizing ages, you could create bins like [0–10, 11–20, 21–30, …]. Another method, called frequency binning (also equal size or equal mass binning) groups the scores by keeping the same number of samples in each Equal Fraction of Data (e. Dataset: 0, 4, 12, 16, 16, 18, 24, 26, 28 I have tried to write a little code for equal width binning but it just produces a histogram. preprocessing import KBinsDiscretizer from feature_engine. Then use the AutoBinner and specify how many bins you want, so if you have 5000 rows, then choose 50 bins for 100 interval width. I found that a search form made it easy to find the latter item using 'binning' as a search term. random. qcut() para binning de frequência igual. 1, 0. The desired data-type for the output. Variations of these methods exist, but they are all essentially based on one of these two approaches. qcut(x, q) function that buckets the continuous feature into q buckets, with equal percentile differences. Each bin span the same number of spectral points: Straightforward and fast to apply. 2], \ldots ,\) (0. . PROC HPBIN enables you to create new Methods for random‐effects meta‐analysis require an estimate of the between‐study variance, τ2. 4. Aug 26, 2020 · Unsupervised binning is a category of binning that transforms a numerical or continuous variable into categorical bins without considering the target class label into account. hist(x, bin_pos) plt. 1], (0. The state-of-the-art method for one-dimensional data infers locally adaptive histograms using the minimum description length (MDL) principle, but the multi-dimensional case is far less studied: current methods consider the dimensions one at a time (if not independently), which result in discretizations based on Jul 5, 2023 · Equal width/binning: the range of the variable is divided into equal-width bins. Unsupervised binning are of two categories: 1. This is of concern because the OP is asking for guidance (a "rule of thumb") about when and how to bin variables. We’ll engineer features from a dataset with information about voter demographics and participation. In the context of image processing, binning is the procedure of combining a cluster of pixels into a single pixel. Unless there are a large number of observations or a complex empirical distribution, the number of bins must be kept small, such as 5-10. The second function always produces very complicated bin boundaries (like, [ (-28. python. Data binning, bucketing is a data pre-processing method used to minimize the effects of small observation errors. import numpy as np. The number of values that fall into each bin will automatically be calculated: From the output we can see: 2 values fall into the 0-5 bin. In particular, you cannot always increase the resolution because there is a limit to the available degrees of freedom. Skip to contents. Step 6: Now, mention the input range. What are some common methods for binning data? Some common methods for binning data include equal width binning, equal frequency binning, and quantile binning. Each question in the series contains a unique solution that might meet the stated goals. Equal Width Binning: Equal Width binning divides the data into bins of equal width. Simon. As such, in 2x2 binning, an array of 4 pixels becomes a single larger pixel, reducing the overall number of pixels. While binning has its advantages, it's important to consider the potential disadvantages that come with using this technique. Consider a dataset containing the heights of 100 individuals. If A and B are the lowest and highest values of the attribute, the Sep 12, 2021 · Binning in Data Mining. With modern statistical methods it is generally not necessary to engage in binning, since anything that can be done on discretized "binned" data May 16, 2023 · The first one, commonly called width binning, distributes scores into a number of bins of the same width, choosing bin edges accordingly (e. The function defines the bins using Mar 3, 2023 · To bin this data you could create equal width bins or bins with a similar number of values assigned to each bin. The qcut function tries to divide up the underlying data into equal sized bins. Mar 8, 2021 · I use pandas for my data analysis task and it has pd. Jun 7, 2022 · In an equal-width histogram, the width of each bucket range is uniform. 5 to 5 feet. cut. The bins size in ppm needs to be specified (0. e. Equal Width Binning Usage binning_eqwid(df, feat, label, nbins = 3) Arguments. The break for an equal-frequency histogram has to be between 4 and 8. This is unnecessary because a larger individual pixel will always capture more raw light. g. Equal Width and Equal Frequency are two unsupervised binning methods. Custom binning Dec 6, 2019 · Width = (maximum value - minimum value) / N * where N is the number of bins or intervals. int : Defines the number of equal-width bins in the range of x. all values between 145 and 215 And for equal width binning you are given number of required bins and in this case it is 3. zk bz yx nu xs cp jf xm mn kv