the Box-and-favorite diagrams, or trace the box, uses the concept of dividing a data set into fourths, or quartiles, to create a display. The coin box of the diagram is based on the middle (the second and third quartiles) of the dataset. The favorites are lines that extend from either side of the box. The maximum length of a favorite is calculated based on the length of the box. The actual length of each bookmark is determined after considering the benchmarks in the first and fourth quartiles. &; # 13; Although the diagrams and box-favorite show less information than histograms or dot plots, they show a lot about distribution, location and dissemination of data represented. They are particularly valuable because many land parcels box can be placed next to each other in a simple chart for easy comparison of multiple data sets. &; # 13; What can it do for you? &; # 13; If your improvement project includes a relatively small amount of different quantitative data, a diagram of box-and-favorite can give you a snapshot of the shape of the variation in your process. Often this can provide immediate insight into the strategies of search you can use to find the cause of this variation. &; # 13; diagrams and box-favorite are particularly meaningful to compare the performance of two processes creating the same feature to track or improve a simple process. They can be used throughout the phases of the methodology of lean six sigma, but you will find diagrams and box-favorite-especially useful in the analysis phase. &; # 13; How do you do? &; # 13; 1. Decide what feature of Critical-To-Quality (CTQ) you want to examine. The CTQ must be measurable on a linear scale. That is, the incremental value between units of measurement must be identical. For example, time, temperature, size and spatial relationships can usually be measured in incremental units complied. &; # 13; 2. Measure the characteristic and record the results. If the feature is produced continuously as the voltage in a line or a temperature in a furnace, or if too many items being produced to measure all you need to take. Be careful to ensure that your sample is random. &; # 13; 3. Count the number of different benchmarks. &; # 13; 4. Identify the landmarks in ascending order. &; # 13; 5. Find the median. If an odd number of landmarks, the median is the point of reference which is halfway between the largest and smallest. (For example, if there are 35 landmarks, the median value is the 18th of benchmarks from the top or bottom of the list.) If there is an even number of points, the median is midway between the two points that occupy the position centermost. (If there had 36 points, the median is halfway between point 18 and point 19. To find the median value, add the values of points 18 and 19, and divide the result by 2.) If you consider the list of benchmarks is divided into quarters (quartiles), the median is the border between the second and the third quartile. &; # 13; Order Boundary Value &; # 13; 1 27. 75 &; # 13; 2 37. 35 &; # 13; 3 38. 35 &; # 13; 4 38. 35 &; # 13; 5 38. 75 &; # 13; Second quartile 39. 250 &, # 13; 6 39. 75 &; # 13; 7 40. 50 &; # 13; 8 41. 00 &; # 13; 9 41. 15 &; # 13; 10 42. 55 &; # 13; Third quartile 42. 725 &, # 13; 11 42. 90 &; # 13; 12 43. 60 &; # 13; 13 43. 85 &; # 13; 14 47. 30 &; # 13; 15 47. 90 &; # 13; Fourth quartile 48. 025 &; # 13; 16 48. 15 &; # 13; 17 49. 86 &; # 13; 18 51. 25 &; # 13; 19 51. 60 &; # 13; 20 56. 00 &; # 13; Data defer divided into quartiles &; # 13; 6. The next step is to find the borders between the first and second and third and fourth quartiles. The first quartile boundary is midway between the lowest point in the first quartile and the first point of reference in the second quartile. (If a point of reference is the median, this benchmark is considered the last point in the second quartile and the first point in the third quartile.) In a similar way, find the third quartile boundary, the point midway between the last value in the third quartile and the first value in the fourth quartile. &; # 13; 7. Draw and mark a line of balanced values. The value of the balance should start lower than your lowest value and extend higher than your highest value. The line of balance can be vertical or horizontal. &; # 13; 8. Using the scale as a guideline, create a box above or to the right balance. One end of the box border will be the first quartile and the other will be the third quartile boundary. (The width of the box is somewhat arbitrary. Boxes tend to be long and thin. As an option, if you have multiple data sets with different numbers of landmarks in each set, make the width of the boxes so that they correspond roughly to the amount of data represented on each box.) &, # 13; 9. Draw a line through the box representing the median (second quartile boundary). &; # 13; 10. The next step is to draw the favorites on the ends of the box. Find the interquartile range (interquartile difference) by subtracting the value of the first quartile boundary from that of the third quartile boundary. &; # 13;    a. The lowest point of benchmarks is greater than or equal to Q1 -1. IQR 5 &; # 13;    b. The biggest point of reference is less than or equal to Q3 1. IQR 5 &; # 13;    c. All items not in the interval [Q1-1. Interquartile difference 5; Q3 1. 5 interquartile difference] are plotted separately. &; # 13; 11. Multiply the difference by quartile 1. 5. (using 1. 5 as a multiplier is a convention that has no exact statistical basis. Multiply by the constant help taking in consideration the fact that the first and fourth quartiles will naturally spread slightly wider than the second and third quartiles.) &, # 13; 12. Subtract the value 1. 5 (interquartile difference) of the value of the first quartile boundary. Find the lowest point of reference in your list of which is equal to or greater than this value. Make a tick mark represents the point of reference to the left of the box (or top if you use a vertical scale). Draw a line, the first favorite on the side of the box to tick mark. &; # 13; 13. Add the value 1. 5 (interquartile difference) to the value of the third quartile boundary. Find the biggest landmark in your list of which is equal to or smaller than this value. Make a tick mark represents the point of reference to the right of the box (or below if you use a vertical scale). Draw another favorite brand for this drill. &; # 13; 14. It is possible that some points in your list of benchmarks will be located outside of the ends of the favorites that you identified in steps 12 and 13. These points are called annexes. Draw all the annexes as points beyond the whiskers. &; # 13; [Note: Steps 3 through 14 are produced automatically if you use Excel, Minitab or JMP to create your diagram Box-and-favorite. If you are familiar with these packages, their use can greatly simplify the process of making diagrams effective box-and-favorite. ] &; # 13; 15. Title and mark your diagram and box-favorite. &; # 13; Now what? &; # 13; The shape of your diagram and box-favorite takes says a lot about your process. &; # 13; One way to help you interpret plots box is to imagine how a data set looking for a histogram is something like a mountain view from ground level and a box-diagram and favorite is something like a map of cutting the mountain as seen from above. &; # 13; In a plot of through histogram and box & Comparative; # 13; The box-second quartile is considerably larger than the box-third quartile, and favorite related to the first quartile extends almost to the end of 1. limit of interquartile difference 5. An annex beyond the 1. limit the interquartile difference of 5 other favorite highlights the fact that the data are strongly biased in that direction. On the other side of the distribution, the favorite in the fourth quartile bound is quite consistent with the 1. interquartile difference 5. In fact, the favorite fourth-quartile range is shorter than the box-third quartile. A histogram of these data show a highly skewed distribution skirting a precipice which fell into the high end of values. Such data sets often occurs when there is a limit to a normal completion of delivery or 100% screening is done to limit specifications. &; # 13; Although diagrams and box-favorite can be oriented horizontally, they more often are shown vertically, with lower values at the bottom of the scale. &; # 13; Compared & normal distribution plot of the curve and box; # 13; Boxes second - and third-quartile are approximately the same size. Favorites are similar to each other in length and extend almost 1. limit of interquartile difference 5. If the data set were actually a combination of two different distributions, for example, material from two suppliers or two machines, it could form a histogram which resembled a plateau or a mountain ridge with binoculars. &; # 13; Histogram & plateau compared to plot box; # 13; The plot of box would show an even distribution, but the boxes have relatively large and relatively short favorites. If there was some data from a different distribution included in the data set, for example, if there was an abnormal process in the short term or error of data collection, the histogram shape resembling a mountain with a small peak isolation. &; # 13; Compared & maximum isolation plot histogram and box; # 13; The plot of box for that data set would look like one for a normal distribution but with a number of annexes beyond a favorite. &; # 13; Some tips & Final; # 13; A diagram of box-and-favorite is a simple way to compare processes and to map the process of improving a process. diagrams and box-favorite can quickly give you a sense of the comparative distribution of data sets. They show the distributional spread by the length of the box and whiskers. &; # 13; Some idea of the symmetry o