Charts
Box-and-whisker, or box plots, use the concept of breaking a whole into
quarters or quartiles data, to create a display. The
whiskers are lines that extend from each side of the box. The
maximum length of whiskers is calculated on the basis of the length of the box.
Although
the box and whisker diagrams provide less information than histograms or
plotted points, they say a lot about the distribution, localization and
distribution for this data. If
your improvement project involves a relatively limited amount of individual
quantitative data, a box and whisker diagram can give you a glimpse of the
shape of variation in the process. Box and whisker plots are particularly
useful for comparing the output of two processes of creating the same
characteristic improvement or follow a single process.
1. Count the
number of individual data points.
2. List of data points in ascending order.
If there are an odd number of data points, the median is the data point that is halfway between the largest and the smallest. (For example, if there are 35 data points, the average value is the value of the data point 18 of the top or bottom of the list.) (If there was 36 points, the median would be halfway between point 18 and point 19. If you think the list of data points being divided into four parts (quartiles), the median is the boundary between the second and third quartile.
Boundary Value End2. List of data points in ascending order.
If there are an odd number of data points, the median is the data point that is halfway between the largest and the smallest. (For example, if there are 35 data points, the average value is the value of the data point 18 of the top or bottom of the list.) (If there was 36 points, the median would be halfway between point 18 and point 19. If you think the list of data points being divided into four parts (quartiles), the median is the boundary between the second and third quartile.
1 27.75
2 37.35
3 38.35
4 38.35
5 38.75
Second quartile 39.250
6 39.75
7 40.50
8 41.00
9 41.15
10 42.55
Third quartile 42.725
11 42.90
12 43.60
13 43.85
14 47.30
15 47.90
Quartile 48.025
16 48.15
17 49.86
18 51.25
19 51.60
20 56.00
Data table divided into quartiles
3. The first quartile threshold is midway between the last data point in the first quartile and the first data point in the second quartile. (If a data point is the average, the data point is considered the last point in the second quartile and the first point in the third quartile). Similarly, find the third quartile boundary, the midpoint between the last value of the third quartile and the first value in the fourth quartile.
4. Draw and label a line of scale values. The scale value should start lower than its lowest value and expand above its highest value. One end of the box is the first quartile boundary; the other will be the third quartile boundary. (The width of the box is somewhat arbitrary. Optionally, if you have multiple data sets with different numbers of data points in each game, the width of the boxes so that they correspond approximately with relative amount of data represented by each box.)
5. Draw a line through the box to represent the median (second quartile boundary).
Find the interquartile range (IQR) by subtracting the threshold value of the first quartile from the third quartile boundary.
a. Minor
data point is greater than or equal to -1.5 Q1 IQR
b. The biggest data point is less than or equal to 1.5 IQR Q3
c. All points that are not in the range [IQR Q1-1.5; Q3 + 1.5 IQR] are plotted separately.
6. Multiply the IQR by 1.5.
b. The biggest data point is less than or equal to 1.5 IQR Q3
c. All points that are not in the range [IQR Q1-1.5; Q3 + 1.5 IQR] are plotted separately.
6. Multiply the IQR by 1.5.
7. Subtract the
value of 1.5 (IQR) from the value of the first quartile threshold. Find
the point of the smallest data in its list which is at or above this value. Make
a check representing the point to the left of your data box (or above, if you
used a vertical scale). Draw
a line, the first mustache on the side of the box to check.
8. Add the value of 1.5 (IQR) for the limit value of the third quartile. Find the largest data point on your list that is less than this value equal to or. Make a check representing this point to the right of your data box (or below, if you used a vertical scale). Draw another whisker to this scale mark.
Tracer outliers as dots beyond the whiskers.
[NOTE: Steps 3-14 to happen automatically if you use Excel, Minitab, JMP or to create your box and whisker diagram. If you're familiar with these programs, their use can greatly simplify the process of preparing the box diagrams effective mustache.]
9. Title and label the box and whisker diagram.
The way your box and whisker diagram takes tells a lot about your process.
In a histogram and plot compared biased box
The second quartile box is considerably larger than the third quartile quartile box associated with the first quartile extends almost to the end of the 1.5 IQR.
8. Add the value of 1.5 (IQR) for the limit value of the third quartile. Find the largest data point on your list that is less than this value equal to or. Make a check representing this point to the right of your data box (or below, if you used a vertical scale). Draw another whisker to this scale mark.
Tracer outliers as dots beyond the whiskers.
[NOTE: Steps 3-14 to happen automatically if you use Excel, Minitab, JMP or to create your box and whisker diagram. If you're familiar with these programs, their use can greatly simplify the process of preparing the box diagrams effective mustache.]
9. Title and label the box and whisker diagram.
The way your box and whisker diagram takes tells a lot about your process.
In a histogram and plot compared biased box
The second quartile box is considerably larger than the third quartile quartile box associated with the first quartile extends almost to the end of the 1.5 IQR.
Normal
distribution curve and comparing the plot box
The second and third quartile zones are approximately the same size.
The second and third quartile zones are approximately the same size.
Comparison
of the histogram and box plot Plateau
The graph of the box show a uniform distribution but have relatively large relatively short box and whisker. If there was a small amount of data from another distribution included in the data set, for example, if there is a short-term process of anomaly or a data collection error, histogram formed seems like a mountain with a small isolated peak.
Isolated peak histogram and box plot compared
The box plot for this data set to look like a normal distribution, but with a number of outliers beyond a close call.
Some final tips
A diagram of the box and whiskers is an easy way to compare processes or to map process improvement in a process. Diagrams Box and whiskers can quickly give you a comparative sense of the distribution of data sets. They show the distribution of the spread over the entire length of the box and whiskers.
Many box plots may be added to an array without creating visual overload.
Not only can box and whisker diagrams help you see which processes need improvement, by comparing the original patterns box plot with the result, they can also help control this improvement.
The graph of the box show a uniform distribution but have relatively large relatively short box and whisker. If there was a small amount of data from another distribution included in the data set, for example, if there is a short-term process of anomaly or a data collection error, histogram formed seems like a mountain with a small isolated peak.
Isolated peak histogram and box plot compared
The box plot for this data set to look like a normal distribution, but with a number of outliers beyond a close call.
Some final tips
A diagram of the box and whiskers is an easy way to compare processes or to map process improvement in a process. Diagrams Box and whiskers can quickly give you a comparative sense of the distribution of data sets. They show the distribution of the spread over the entire length of the box and whiskers.
Many box plots may be added to an array without creating visual overload.
Not only can box and whisker diagrams help you see which processes need improvement, by comparing the original patterns box plot with the result, they can also help control this improvement.
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