![]() Showing averages over time or across some series of data often allows us to answer questions like: How long did the app take to load in the mobile device? To answer this question, most commonly, we would find all data points for the day and then compute the average. But when you have diverse data points and sources, telling the story with just one aggregation to represent the whole range of numbers might often not tell the fully story. The Box and Whisker charts are a great tool for a quick look at how several processes compare.By Amir Netz, Technical Fellow and Mey Meenakshisundaram, Product Manager Houston is the hottest on average New York City the coldest, though it does get hotter at times than San Francisco. It is easy to see that New York City has more variation in temperature than the other two cities. You can make a Box and Whisker chart for each of these cities as was done in the chart above. You can use a Box and Whisker plot to compare the variation and medians in multiple processes. ![]() The resulting Box and Whisker plot for these data is shown below. The earlier versions of the SPC for Excel software did this later versions use the calculations at this link. Note: the Quartile function in Excel can be used to find Q1 and Q3. If you have data points outside this they will show up as outliers. The whiskers cannot extend any further than 1.5 times the length of the inner quartiles.The 75th quartile is where, at most, 25% of the data is above it.The 25th quartile is where, at most, 25% of the data fall below it.The median is the point where 50% of the data is above it and 50% below it.The box represents the middle 50% of the data.This box and whisker plot provides a 5 point summary of the data. This means that Q3 lies between the eleventh and twelfth data points. The third quartile is the kth observation where k = (3n+1)/4. Since k = 4.5, the value of Q1 is halfway between these two values. The fourth data point is 72 and the fifth data point is 74. Remember, the data must be in ascending order. This means that Q1 lies between the fourth and fifth data point. In this example, there are 15 data points. Linear interpolation is used if k is not an integer. The first quartile is the kth observation when the data is arranged in ascending order and k = (n+3)/4. We will use the method developed by Emil Gumbel for determining quartiles. 75% of the values in the data set are less than this value. ![]() The 75th quartile is the third quartile (Q3). 25% of the values in the data set are less than this value. The lower quartile (the 25th) is first quartile (Q1). A quartile is defined as the value of the boundary at the 25th, 50th, or 75th percentiles of a frequency distribution divided into four parts, each containing a quarter of the population. Unfortunately, there are about ten methods for determining the quartiles. There is agreement on how to find the median. It should be noted that if there is an even number of data points, the median is the average of the middle two. There are seven values above it and seven values below it. The median is the middle point of a data set 50% of the values are below this point, and 50% are above this point.
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