Lecture 27 about the graphical methods. By the end of this lecture, you will learn about stem and leaf plots, box and whisker plots, run charts, etc. In the previous chapter, we learned about different types of data, type of measurement scales, methods of collecting data, etc. as well as we learned to describe the data using statistical methods such as mean and standard deviation. Now, we will learn about The various graphical methods of describing a set of data. First of all, the stem and leaf method, stem and leaf is a graphical method of describing a set of data, especially when the data is grouped.

Let us take an example of some measurement data from one of the six sigma projects. The data is as you see on the screen in one glance, could you say something about this data set. It is difficult to commend at one glance The simple way of describing the data is to arrange the data either in ascending or descending order. I have arrange the data in ascending order. It looks nice now, isn't it? We can see at one glance that lowest and highest value in the data set is 0.11 and 0.49 respectively.

Now, let us group the data say the data falling in the range from 0.102 0.19 similarly, grouped the data from 0.20 to 0.29 and so on. Now, for making a stem and leaf graph, take the largest place value from one group in the first group, it is 0.1. Now, place this value under the stem now pick the remaining place value form Once set and place them in ascending order under the leaf column. That means, in the first group there are four data values 0.11 0.18 0.18 and 0.19 respectively. If we take the least place value from each data, we can put 188 and nine respectively, as you can see on the screen now repeat it with other data groups to complete the stem and leaf plot. Run chart is another graphical method that describes us set of data in a fixed time interval.

For example, let us see the plot for number of customer complaints per 30 minutes at a call center. The graph reads such as till eight o'clock, there were seven complaints from eight to 830 there were five complaints from 11 to 1130. There were three complaints, etc etc. let us study about an important tool of Six Sigma the boxplot what is a box plot? boxplot is a tool that provides a graphical summary of the pattern of variation. It is especially useful when working with small set of data.

And when comparing many different situations boxplot of any data set can be understood by its five elements. Number one, the lowest value in the data set number two, the first quartile, that is the point below which 25% of data fall number three, median, the middle value and the set of data. We have learned in previous lectures that median is also one of the measure of central tendency number for third quartile the point under which the 75% of the data fall and number five, the largest value in the set of data. Let us learn it by doing it in one of the six sigma projects, the team wanted to analyze that whether there is a performance variation between two of their AMC contractors, namely a and b the team collected The response time in minutes for both the contractors and as shown on the screen once again let me ask what could you comment on this data in one glance okay.

Difficult to command in one glance, best way is to arrange them in ascending order. Now, we can see the lowest and highest response time by each contractors. Next step is to find the median. The calculation for median is d of m is equal to n plus one divided by two where n denotes the number of observation and a set of data to calculate the median for contractor a, we need to find out the position of median and the data set that is d of m that is 10 plus one divided by two that is equal to 5.5 that means, the median lies and the five point fifth position the data at fifth position is 233. Hence, to find out the data of five point fifth position it will be equal to 233 plus 0.5 multiplied by 241 minus 233 that is equal to 247 that means, the median response time of contractor A is equal to two for seven minutes.

Similarly, we can calculate the median response time for contractor B, which comes as 180 minutes. Now, to find out the first the third quarter isles respect tively The formula is first quarter mile D of q1 is equal to one into n plus two divided by four that is equal to three for contractor a third quarter mile D of q3 is equals to three into n plus two divided by four, that is equal to eight for contractor B. Now, we can find out the data at third and eighth position to find out the first and third quarter respectively. Now, Get all the required elements of a boxplot such as median first quarter, third quarter mile west value, highest value or drawing the boxplot at the x axis, plot the contractors at y axis, the response time and minutes. Now plot the highest and lowest value of contractor A, then plot the first and third quarter notes.

Now, draw a box with first and third core tiles Next is to plot the median of contractor a. Now, we can plot similar graph for contractor B to now, let us analyze the boxplot and find out which contractor is better median response time of B is 180 minutes median response time of A is to 37 minutes. variation in his response time is greater than b fastest response time was of a but that does not mean performance of Team A better because only about 25% of team a response time are less than 197 minutes whereas 75% of the team be response time are less than two to eight minutes. Nearly 25% of team a response time are longer than these longest response time. With this comparison, we can conclude that DB performance is better than of Team A. Let us learn boxplot in Minitab.

Double click on three point box plots. After downloading. Click graph boxplot the box plot dialog box will open. Click one y simple and click OK. You can also click multiple why's simple and click OK to draw box plots of both contractors together as we did it in the above example the boxplot one y sample dialog box will open. Double click on Team A and click OK. box plot graph window will open analyze the graph to Exercise 14 be by yourself. That's all for this lecture.

Let us proceed to the next lecture on other graphical methods based on the blk three, C five