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Distribution of Data The following terms are commonly used to describe the distribution of data. Describing Data: The left and right side look the same, so the data is symmetric. There is a cluster from 31-39. There are no gaps or outliers, and the peak is at 35. The distribution of a set of data shows the arrangement of the values. It is described by its center, spread (a description of the variation of the values within the set), and overall shape. The terms symmetric, gaps, clusters, and outlier are used to describe the shape of the data. Mean deviation or IQ Range Mean, median, or mode The data on the right is not symmetric. It has gaps at 9 and 13. There is a cluster from 10-12. There are no outliers. Is this data symmetric? Are there outliers? The data is kind of symmetricβ¦.. There are no outliers. Where are the gaps? The gap is from 19-21. Where is the peak? The peak is at 22. A box plot does not allow for the detail of any gaps. We cannot determine the peak. We can see there are no outliers as the whiskers are about the same size. The data is symmetrical. We can see the data is not symmetrical. There are no gaps. The cluster of the data is from :01 to 7:30. The peak is the :01 β 2:30 time interval. What is being measured? What units are used? The data is not symmetric. There is an outlier. median What would be the preferred measure of center? The data is not symmetric. This, along with the presence of the outlier would make the interquartile range the best way to describe the spread of the data. What are the measures of variation??????? There are 19 values. 12 Median _________ 11 Lower Quartile ____________ 13 Upper Quartile _______________ IQ Range _____ 2 10 10 10 11 11 11 11 11 12 12 12 12 12 12 13 13 13 14 19 How many people responded to this survey? Clusters: 0-49 minutes Peak: 20-29 Gap: 50-89 Outlier: 90-99 The data is NOT symmetrical. The outlier is 20. Notice the way the outlier is indicated on this box plot. You would use the median and IQ Range as measures to represent this data. a) The data is symmetrical. There are no gaps or outliers. There is a peak at 4. This distribution would indicate that the mean and absolute mean deviation would be the best measures to represent this data. We will find both measures. The mean and absolute mean deviation would be the appropriate measures to describe the center and spread of the distribution. Mean = πππ ππ Mean = ππ ππ Mean = 4 1 + 4 + 9 + 20 + 15 + 12 + 7 4 3+4+3+0+3+4+3 Absolute mean deviation = Absolute mean deviation = 3+4+3+0+3+4+3 ππ 20 ππ Absolute mean deviation = 1.2 What have we done β’ We have described the shape of data. β’ Based on the shape of the data, we have chosen the appropriate measures of center and spread.
