Histogram (Flexi)

What is Histogram?

A histogram is a graphical representation of the distribution of numerical data. It consists of a series of bars, where each bar represents a range of values and the height of the bar corresponds to the frequency or count of values within that range.

They are commonly used to visualize the frequency distribution of continuous or discrete data. The horizontal axis represents the range of values, divided into equally spaced intervals called bins. The vertical axis represents the frequency or count of values falling within each bin.

When to use Histogram?

Here are some situations where they are particularly useful:

  • Data Distribution Analysis: It provides a visual representation of the frequency distribution of data. They help you understand the shape of the distribution, identify the central tendency (mean, median, mode), and assess the spread or variability of the data. It can reveal patterns such as normal distribution, skewed distribution, bimodal distribution, or outliers.
  • Data Exploration: They are useful for exploring a dataset and gaining insights into the values it contains. They allow you to see the frequency and concentration of values within specific ranges or bins. This can help you identify clusters, gaps, or unusual patterns in the data.
  • Outlier Detection: It can help you identify outliers or extreme values in a dataset. Outliers are often visible as bars that are significantly taller or shorter than the rest of the bars. By examining the tails or extreme ends of the histogram, you can spot values that deviate from the main distribution.
  • Data Preprocessing: It can aid in data preprocessing tasks. For example, they can be used to assess the distributional characteristics of a variable before deciding on appropriate data transformations, such as normalization or log transformations. It can also help in determining the optimal binning strategy for discretizing continuous variables.
  • Comparison of Distributions: They are useful for comparing the distributions of different variables or datasets. By plotting multiple histograms on the same graph, you can visually compare their shapes, ranges, and central tendencies. This can be helpful in identifying similarities, differences, or relationships between variables.
  • Quality Control and Process Improvement: It widely used in quality control to monitor and improve processes. They can be used to visualize process output data and assess whether it meets desired specifications or falls within acceptable limits. Deviations or abnormalities in the histogram can indicate potential issues or opportunities for improvement.

Guidelines for correct usage of Histogram

  • Sample size should be 20 or greater for effective representation of data
  • They are suitable when sample size is at least 20
  • Small sample sizes may lead to insufficient data in each histogram bar
  • Consider using Individual value plot if sample size is less than 20
  • Random selection of sample data is important
  • Random samples allow for generalizations and inferences about the population
  • Non-randomly collected data may not accurately represent the population.

Alternatives: When not to use Histogram

  • Individual Value Plot: If the sample size is smaller than 20, it is advisable to opt for an Individual value plot as an alternative.

Example of Histogram (Flexi)?

In order to verify the proper fastening of shampoo bottle caps, a quality control engineer must ensure that they are neither too loose nor too tight. If the caps are not securely fastened, they may fall off during shipping, while excessively tight caps may be difficult to remove. To assess the torque required to remove the caps, the engineer gathers a random sample of 68 bottles and performs tests.

As part of the initial investigation, the engineer constructs a histogram of the torque measurements to examine the distribution of the data. She has performed this in following steps:

  1. She worked all day and gathered the necessary data.
  2. Now, she analyzes the data with the help of https://qtools.zometric.com/
  3. Inside the tool, she feeds the data.
  4. After using the above mentioned tool, she fetches the output as follows:

How to do Histogram (Flexi)

The guide is as follows:

  1. Login in to QTools account with the help of https://qtools.zometric.com/
  2. On the home page, you can see Histogram (Flexi) under Graphical Analysis.
  3. Click on Histogram (Flexi) and reach the dashboard.
  4. Next, update the data manually or can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.
  5. Next, you need to map the parameters with the appropriate columns.
  6. Finally, click on calculate at the bottom of the page and you will get desired results.

On the dashboard of Histogram (Flexi), the window is separated into two parts.

On the left part, Data Pane is present. In the Data Pane, each row makes one subgroup. Data can be fed manually or the one can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.

On the right part, there are many options present as follows:

  • Histnorm:
    • Count: It represents the count or frequency of data points in each bin. Each bin's height represents the number of data points falling within that bin.
    • Percent: Each bin's height represents the percentage of data points relative to the total number of data points in the dataset.
    • Probability: Each bin's height represents the probability of a data point falling within that bin. The sum of all bin heights will equal 1.
    • Probability Density: The probability density histnorm calculates the probability density function (PDF) by normalizing the histogram counts such that the area under the histogram equals 1.
  • Marginal: In the context of histograms, "marginal" typically refers to the individual distribution of a single variable, represented by a histogram, without considering the relationship or interactions with other variables.

Example of Histogram Distplot?

A quality engineer is conducting a comparison between pistons from two different suppliers. The engineer randomly selects and measures the lengths of 100 pistons from each supplier. To compare the distributions of the sample data, the engineer creates a histogram with fit and groups. She has performed this in following steps:

  1. She worked all day and gathered the necessary data.
  2. Now, she analyzes the data with the help of https://qtools.zometric.com/
  3. Inside the tool, she feeds the data. Also, she keeps bin size as 1, histnorm as probability density and curve type as normal.
  4. After using the above mentioned tool, she fetches the output as follows:

How to do Histogram Distplot

The guide is as follows:

  1. Login in to QTools account with the help of https://qtools.zometric.com/
  2. On the home page, you can see Histogram Distplot under Graphical Analysis.
  3. Click on Histogram Distplot and reach the dashboard.
  4. Next, update the data manually or can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.
  5. Next, you need to put the value of bin size as 1.
  6. Finally, click on calculate at the bottom of the page and you will get desired results.

On the dashboard of Histogram Distplot, the window is separated into two parts.

On the left part, Data Pane is present. In the Data Pane, each row makes one subgroup. Data can be fed manually or the one can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.

On the right part, there are many options present as follows:

  • Histnorm:
    • Probability: Each bin's height represents the probability of a data point falling within that bin. The sum of all bin heights will equal 1.
    • Probability Density: The probability density histnorm calculates the probability density function (PDF) by normalizing the histogram counts such that the area under the histogram equals 1.
  • Bin Size: The bin size, also known as bin width or bin interval, refers to the width of each interval or bin used in a histogram. When constructing a histogram, the data range is divided into a set of equal-sized intervals, and the number of data points falling into each interval is counted to create the histogram.
  • Curve type:
    • KDE: In the context of histograms, the "kde" curve type refers to the Kernel Density Estimation curve. While histograms display the distribution of data through bins and bars, a KDE curve provides a smooth estimate of the underlying probability density function (PDF) of the data.
    • Normal: In the context of histograms, the "normal" curve type refers to the normal distribution curve, also known as the Gaussian curve or bell curve. The normal distribution is a symmetric probability distribution that is widely used in statistics and probability theory.