Histogram | Different Types | Patterns | Examples | Case Study

 What is a Histogram?

→ Histogram is a bar chart representing the variable data's frequency distribution.

→ Only one parameter can be used to construct this chart.

→ It is one of the most important frequency distribution tools of the 7 QC Tools.

→ The parameter must be variable data such as weight, time, temperature, dimensions, speed, etc.

→ Histogram is a key tool for the Lean Six Sigma Project for the graphical representation of variable data.

Table of Contents:

• What is a Histogram?
• Key Concept of Histogram
• When to Use Histogram?
• Why to Use Histogram?
• How to Make a Histogram?
• Examples of Histogram Patterns
• Normal Distribution Pattern
• Skewed Distribution Pattern
• Double Peaked or Bi-model Pattern
• Multi Peaked or Multi-model Pattern
• Edge Peaked Pattern
• Truncated or Heart-cut Pattern
• Limitations of Histogram
• Benefits of Histogram
• Conclusion

Key Concept of Histogram:

⏩The Key Concept is:

→ Data always have a variation.

→ Variation has a Pattern.

→ Patterns can be seen easily when summarized pictorially.

→ A histogram is similar to a bar graph.

→ The basic difference between the bar graph and histogram is that a bar graph correlates a value with a single category or discrete variable, while a histogram visualizes frequencies for continuous variables.

When to Use Histogram?

→ Histogram is used when:

• The data is variable or numerical.
• We need a graphical representation of large data.
• Observe the process changes with respect to time.
• We need to fulfill customer-specific requirements.
• It is also used as a decision-making tool.
• Problem forecasting.
• Study the variation in the ongoing process.

Why to Use Histogram?

→ A histogram is a powerful tool for visualizing data and provides valuable insights into data analysis.

⏩We can use histograms for several important reasons such as:

→ A histogram is very useful for understanding data distribution such as shape, spread, central tendency, outliers, etc...

→ It allows us to comparison of different data sets.

→ Good decision-making tool and simple to use.

→ We can use this chart across various domains such as manufacturing, quality, market research, financial analysis, etc.

→ It is used for departmental or business presentations.

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How to Make a Histogram?

→ Histogram is very easy to draw with the help of variable data.

→ Now we will learn step by step approach to making this chart.

⏩Refer to the below-mentioned Seven Steps for making a histogram:

1. Data Collection
2. Compute the Range
3. Determine the number of intervals
4. Determine the interval width
5. Summarize the record
6. Construct the Graph
7. Analyze the pattern of the chart

→ Now we will go through each step in detail with an example.

(1) Data Collection:

→ The first step is to collect data to prepare the graph.

→ For better analysis and forecasting of the process collect at least 100 record points.

→ Now for better understanding, we take an example of 150 record points for making a chart.

→ Refer to the below picture that shows the collected 150 data points.

(2) Calculate the Range:

→ After data collection, we will calculate the range of the collected readings.

→ For range calculation we will find the gap between the largest value and the smallest value.

→ Largest Value     = 442

→ Smallest Value   = 204

→ Range of Values =  442-204 = 238

(3) Determine the No. of intervals required:

→ Now after calculation of the range, we need to identify how many intervals are needed for our process and collected readings.

→ So in this step, we will find the number of intervals required.

→ Refer to the chart given in the picture below, we have collected the 150 recorded.

→ So we need 7 to 12 intervals to construct the chart.

(4) Determine the interval width:

→ After deciding the number of intervals, we now need to calculate the interval width.

→ As mentioned in the below picture we will calculate the interval width with the help of a simple formula.

→ Interval width = (Range/No. of interval)

→ Interval width is also known as a bin.

(5) Summarize the record:

→ Till now, we have collected the data, calculated the range, identified no. the intervals, and calculated the interval width.

→ Now we will be moving towards summarizing the data as per the interval.

→ And count the frequency as per the range value for the construction of the graph.

(6) Construct the Graph:

→ Now we will have all data ready for constructing the graph.

→ Refer to the below picture for how the graph looks like.

⏩Five Key Elements of Histogram:

1. Suitable title
2. Y-axis/Vertical axis = Interval width,
3. X-axis/Horizontal axis = Interval width,
4. Graph - Trendline, and
5. Legend (if applicable)

→ Study the below picture for a better understanding.

(07) Analyze the Graph pattern:

→ The last and final step is to interpretation of the graph.

⏩We will interpret below key criteria below in the histogram:

• Central Tendency
• Process Variation
• Graph Shape
• Process Capability (Comparison with the specification)

→ Moving forward we will learn different patterns with examples.

Examples of Histogram Patterns:

→ Now we will learn about the different types of patterns with examples.

→ Different patterns can be classified into different types based on the frequency distribution of the data.

⏩Different types of histogram patterns are:

1. Normal Distribution Pattern
2. Skewed Distribution Pattern
3. Double Peaked or Bi-model Pattern
4. Multi Peaked or Multi-model Pattern
5. Edge Peaked Pattern
6. Truncated or Heart-cut Pattern

→ Now we will learn one by one patterns with examples.

(1) Normal Distribution:

→ Normal Distribution looks like a bell-shaped curve.

→ It is also called a symmetric histogram.

→ In this chart pattern, the peak is in the middle of the graph.

→ When we draw the vertical line from the upper top to down the center of the chart, and we find both sides are identical in size and shape, then we can say that this is a symmetric or normal distribution pattern.

→ In a normal distribution chart, the right half of the diagram is perfectly symmetric with the left half of the diagram.

(2) Skewed Distribution:

→ When the histograms that are not symmetric are known as skewed distribution.

→ In this chart a peak is off-center either right or left

→ Analysis of very pure products is skewed i.e. product cannot be more than 100% pure.

→ When the range is not set properly for operation at that time we can also get skewed distribution.

→ Sometimes this graph is right-skewed or left-skewed according to the direction of the tail.

(3) Double-Peaked / Bi-modal:

→ The chart pattern contains two peaks so it is called a double-peaked or bi-model chart.

→ It shows two Bell-shaped distributions.

→ This chart pattern is formed while a combination of records of two processes or two shifts is mixed.

(4) Multi Peaked / Multi-modal:

→ The multi-model distribution is also known as the plateau distribution.

→ The bimodal distribution looks like the back of a two-humped camel.

→ When different processes with normal distribution are put together then it will create the multi-peak pattern.

→ We can also say that the readings of several processes are plotted on the same graph.

→ Sometimes this kind of graph is formed during a mix of two shifts of data.

→ Another reason for this graph is the range selection is not proper.

(5) Edge Peaked:

→ This distribution looks like a normal distribution with a bigger peak at one tail.

→ Generally, it happens during the wrong construction of the histogram.

→ Sometimes this pattern happens at borderline doubt for inspection and take it as ok.

→ Also in some cases the instrument error is also responsible for this type of graph.

(6) Truncated or Heart-cut:

→ This distribution looks like a normal distribution with the tails being cut off.

→ This pattern forms during mixed of parts that are within specification and out of the specification limit.

→ Sometimes suppliers send a mixed lot of any part and during 100% of incoming inspections, we found this type of graph.

Limitations of Histogram:

• We can not plot individual data points into a graph
• It is very sensitive to bin size (interval size)
• Not suitable for a small data set
• It does not provide cumulative information
• Difficult to plot continuous data in graph
• It does not work with multiple variables at a time
• This graph is static in nature 

Benefits of Histogram:

• Summarize Large data set Graphically
• Confirms measurements to Specification
• Excellent problem-forecasting tool in the process
• Assist with decision-making in the ongoing process
• Identify data patterns and trends
• It is very easy to use and understand
• Useful for data analysis such as shape, spread, central tendency, outliers, etc...
• We can use it in the different departments and processes.
• It is very useful for pictorial representation of data

Conclusion:

→ A histogram is a necessary tool for data analysis and visualization.

→ It offers a unique way to represent the dataset in the graph.

→ It enables quick identification of patterns, trends, and outliers.

→ That helps us with decision-making and problem-solving.

→ We can use histograms with another statistical tool to systematically view data, trends, and patterns.

→ Finally, it is very easy to use and understand.