Continuous Improvement Toolkit Histogram www. citoolkit .com
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Histogram One of the best ways to analyze any process is to plot the data X X X X X X X X X X X * www. citoolkit .com
Histogram A histogram is a graphical way that summarizes the important aspects of the distribution of continuous data It is a type of bar chart www. citoolkit .com
Histogram Histograms are sometimes called Frequency Plots as they show the frequency of continuous data values on a graph Number of occurrence (frequency) | ––––––––– Value bins ––––––––– | While Pareto charts plot the frequency of count data www. citoolkit .com
Histogram Histograms can be drawn either vertically or horizontally | –––––– Frequency –––––– | | –––––– Frequency –––––– | The height of the column indicates how often that data value occurred www. citoolkit .com
Histogram Histograms are widely used in statistics, process improvement, scientific research, economics, and in social and human sciences Mainly used to explore data as well as to present the data in an easy and understandable manner. www. citoolkit .com
Histogram It allows to visually and quickly assess . . . The shape of the distribution The central tendency and the amount of spread in the data The presence of gaps , outliers or unusual data points * Center Spread Gap Outliers www. citoolkit .com
Histogram Shows where most of the data exists * Center Spread Outliers www. citoolkit .com
Histogram Creates a picture of the variation in a process Enables to quickly identify the spread of the data * Center Spread Outliers www. citoolkit .com
Histogram * Center Overall shape shows how the data is Spread Outliers distributed www. citoolkit .com
Histogram * Helps to find unusual Center data points and outliers that may need further investigation Spread Outliers www. citoolkit .com
Histogram Enables to quickly identify the spread of the data Shows where most of the data exists * Helps to find unusual Center data points and outliers that may need further investigation Overall shape shows how the data is Spread Outliers distributed www. citoolkit .com
Histogram Plotting data in a histogram allows to know . . . Minimum and maximum values Gaps and outliers The shape of data (symmetric or skewed) Whether it’s unimodal, bimodal or multimodal www. citoolkit .com
Histogram Used as the first step to determine the underlying probability distribution of a data set A way to shape the sample data to make predictions and draw conclusions about an entire population www. citoolkit .com
Histogram Histograms are used to identify . . . Patterns that provide clues to certain types of problems Whether you can apply certain statistical tests Whether variability is within specification limits Whether the process is capable or not Whether there is a shift in the process www. citoolkit .com
Histogram Used to verify that the changes made were a real improvement Before After www. citoolkit .com
Histogram Ideal to represent moderate to large amount of data N = 40 N = 14 In practice, a sample size of at least 30 data values would be sufficient www. citoolkit .com
Histogram It may not accurately display the distribution shape if the data size is too small Dot plots are preferred over histograms when representing small amount of data www. citoolkit .com
Histogram How to Construct a Histogram Collect the data set and prepare it for the analysis C r e a t e a s u m m a r y t a b l e o f t h e d a t a Data www. citoolkit .com
Histogram How to Construct a Histogram Draw a horizontal line and divide it into equal intervals or bins (between 7 to 10 intervals) T h e t o t a l w i d t h s h o u l d b e e q u a l t o t h e r a n g e o f t h e d a t a www. citoolkit .com
Histogram How to Construct a Histogram Draw bars above each bin to represent the frequency of the data values within each interval T h e b a r s s h o u l d b e a d j a c e n t w i t h n o g a p s b e t w e e n t h e m ( t o i n d i c a t e t h e c o n t i n u i t y o f t h e d a t a ) www. citoolkit .com
Histogram How to Construct a Histogram Indicate the mean of the data and other important information S u c h a s t h e s t a n d a r d d e v i a t i o n a n d t h e s p e c i f i c a t i o n l i m i t s Mean www. citoolkit .com
Histogram Example – Cable Diameters Mean 0.5465 StDev 0.01934 20 N 100 Data source: Minitab 1 5 Frequency 1 0 5 0 0.50 0.52 0.54 0.56 0.58 0.60 Diameter of cable www. citoolkit .com
Histogram Example – Cable Diameters The result can be summarized using 0 day to day language such as: 5 “The distribution looks symmetric 0 around the cable diameter mean (0.546 cm) and appears to fit the 5 Normal Distribution” . 0 0.50 0.52 0.54 0.56 0.58 0.60 Data source: Minitab www. citoolkit .com
Histogram Example – Presence of Diabetes Mean 99.65 StDev 36.58 N 310 www. citoolkit .com
Histogram Example – Presence of Diabetes The distribution of the data is skewed to the right . The distribution is more like an exponential distribution which is normal for this type of data. www. citoolkit .com
Histogram Further Information Histograms like control charts can be used to assess improvement overtime Histograms, however, can’t see changes and trends over time www. citoolkit .com
Histogram Further Information You can illustrate a stratification factor in histograms Night shift Morning shift Evening shift www. citoolkit .com
Histogram Further Information There are many applications and online services that allow the creation of histograms quickly and automatically (such as Minitab, JMP, and SPSS) www. citoolkit .com
Histogram Further Information – One of the 7 Basic Tools of Quality www. citoolkit .com
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