A histogram visualizes the distribution of data over a continuous interval or certain time period. Read more about this chart here. In statistics, a Histogram is a graphical display of the form to show the distribution of the data visually or how often a different value that occur in a given set of data. The histogram is also one of the tools of the 7 tools quality control (QC 7 Tools).
Benefits from the use of the Histogram is to provide information about the variation in processes and assist management in making decisions in an attempt to increase the secure process (Continuous Process Improvement).
The following are the steps needed to create a Histogram:
The data to create the Histogram data is in the form of Numerical measurements.
As an example:
An Engineer wants to collect data for the measurement of the length of the foot of A component such as the table below:
Before determining the magnitude of the value Range, we need to know the value of the largest and Smallest Value from all our measurement data. How to calculate the value of the Range (R) are:
R = XMax – Xmins
or
Range = the greatest value – the value of the smallest
Note:
If you are using Excel, you can use Function:
Find the greatest value: @MAX (initial cell number: cell number end)
looking for the smallest Value: @MIN (initial cell number: cell number end)
For the example above, the magnitude of the Value Range is 0.6 with the calculation below:
Range = 3.2 – 2.6
Range = 0.6
As a guideline, there are tables which determine his appropriate Interval Class with a large number of Sample units of Measurement Data.
For the example case above, the number of sample measurement data is 50 data, then we select the number of the class interval is 7 fruit (according to table is 6 to 10).
4.1. Determining the width of a class Interval
That determines the width of each class Interval is a division of Range (step 2) and the number of Interval classes (step 3).
The same case, for calculating the width of the Class Intervals are:
A. Width = Range/Class Interval
B. Width = 0.6/7
C. Width = 0.1 (rounded)
4.2. Determining Limits for each class Interval
To determine the Limits for each class Interval, we wear formula:
The lowest value – ½ x units of measurement
(in this case we wear measurement of 0.1 units)
First Class Limit:
Specifies the lower limit of the first class:
2.6 – ½ x 0.1 = 2.55
Next lower limit of first class plus the width of the Class Intervals to determine the upper limit of the first class:
2.55 + 0.1 = 2.65
Second Class Limit:
Specifies the lower limit of second class:
lower limit upper limit of second is first class, IE: 2.65
Second upper limit lower limit is the second coupled with the width of the Class Intervals are: 2.65 + 0.1 = 2.75
Third Grade Boundaries and beyond:
Proceed to the third grade and so on as a way to determine the limit of second class.
4.3. Determining the value of the middle of each Class Interval:
The Middle Value Of The First Class:
The middle value of a first class = upper limit lower limit + first class/2
= 2.55 + 2.65/2
= 2.6
The middle value of the second class and so on:
The middle value of the second class and so on uses the same way as calculating the Middle Class first.
To simplify the calculation, use the sign "Tally" grouping 5 (five) to count one by one the number of frequencies that fall within class intervals.
Still the same case, the following table results of calculations:
Above is the Manual way in calculation and graphing the Histogram. In the market, there are many special Statistics Software can do so very easily. Including Software Mini tab very popular among practitioners of statistics, especially those associated with Process Improvement Methodologies such as Six Sigma and more.
Benefits from the use of the Histogram is to provide information about the variation in processes and assist management in making decisions in an attempt to increase the secure process (Continuous Process Improvement).
The steps in making a Histogram:
The following are the steps needed to create a Histogram:
1. Collect data Measurement
The data to create the Histogram data is in the form of Numerical measurements.
As an example:
An Engineer wants to collect data for the measurement of the length of the foot of A component such as the table below:
2. Determine the magnitude Range
Before determining the magnitude of the value Range, we need to know the value of the largest and Smallest Value from all our measurement data. How to calculate the value of the Range (R) are:
R = XMax – Xmins
or
Range = the greatest value – the value of the smallest
Note:
If you are using Excel, you can use Function:
Find the greatest value: @MAX (initial cell number: cell number end)
looking for the smallest Value: @MIN (initial cell number: cell number end)
For the example above, the magnitude of the Value Range is 0.6 with the calculation below:
Range = 3.2 – 2.6
Range = 0.6
3. Determine the number of class Intervals
As a guideline, there are tables which determine his appropriate Interval Class with a large number of Sample units of Measurement Data.
For the example case above, the number of sample measurement data is 50 data, then we select the number of the class interval is 7 fruit (according to table is 6 to 10).
4. Determine the width of the Class intervals, Limit Value class, and the Middle Class
4.1. Determining the width of a class Interval
That determines the width of each class Interval is a division of Range (step 2) and the number of Interval classes (step 3).
The same case, for calculating the width of the Class Intervals are:
A. Width = Range/Class Interval
B. Width = 0.6/7
C. Width = 0.1 (rounded)
4.2. Determining Limits for each class Interval
To determine the Limits for each class Interval, we wear formula:
The lowest value – ½ x units of measurement
(in this case we wear measurement of 0.1 units)
First Class Limit:
Specifies the lower limit of the first class:
2.6 – ½ x 0.1 = 2.55
Next lower limit of first class plus the width of the Class Intervals to determine the upper limit of the first class:
2.55 + 0.1 = 2.65
Second Class Limit:
Specifies the lower limit of second class:
lower limit upper limit of second is first class, IE: 2.65
Second upper limit lower limit is the second coupled with the width of the Class Intervals are: 2.65 + 0.1 = 2.75
Third Grade Boundaries and beyond:
Proceed to the third grade and so on as a way to determine the limit of second class.
4.3. Determining the value of the middle of each Class Interval:
The Middle Value Of The First Class:
The middle value of a first class = upper limit lower limit + first class/2
= 2.55 + 2.65/2
= 2.6
The middle value of the second class and so on:
The middle value of the second class and so on uses the same way as calculating the Middle Class first.
5. Determine the frequency of each class Interval
To simplify the calculation, use the sign "Tally" grouping 5 (five) to count one by one the number of frequencies that fall within class intervals.
Still the same case, the following table results of calculations:
- Graph a Histogram
- Make a Horizontal line by using a scale based on the units of measurement data
- Make a vertical line using frequency scale
- Describe the bar graph, the height in accordance with the frequency of each class Interval
- If there is a limitation of the specification defined by the Customer (customers) then pull the vertical line corresponds to the specification.
Above is the Manual way in calculation and graphing the Histogram. In the market, there are many special Statistics Software can do so very easily. Including Software Mini tab very popular among practitioners of statistics, especially those associated with Process Improvement Methodologies such as Six Sigma and more.
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