If the distribution of data is skewed to the right, the mode is often less than the median, which is less than the mean. To summarize, generally if the distribution of data is skewed to the left, the mean is less than the median, which is often less than the mode. Again, the mean reflects the skewing the most. Of the three statistics, the mean is the largest, while the mode is the smallest. The mean is 7.7, the median is 7.5, and the mode is seven. The histogram for the data: 6 7 7 7 7 8 8 8 9 10, is also not symmetrical. The mean and the median both reflect the skewing, but the mean reflects it more so. Notice that the mean is less than the median, and they are both less than the mode. The mean is 6.3, the median is 6.5, and the mode is seven. A distribution of this type is called skewed to the left because it is pulled out to the left. The right-hand side seems “chopped off” compared to the left side. The histogram for the data: 4 5 6 6 6 7 7 7 7 8 is not symmetrical. In a symmetrical distribution that has two modes (bimodal), the two modes would be different from the mean and median. This example has one mode (unimodal), and the mode is the same as the mean and median. In a perfectly symmetrical distribution, the mean and the median are the same. The mean, the median, and the mode are each seven for these data. A distribution is symmetrical if a vertical line can be drawn at some point in the histogram such that the shape to the left and the right of the vertical line are mirror images of each other. The histogram displays a symmetrical distribution of data. Each interval has width one, and each value is located in the middle of an interval. This data set can be represented by following histogram. Recognize, describe, and calculate the measures of the center of data: mean, median, and mode.Ĥ 5 6 6 6 7 7 7 7 7 7 8 8 8 9 10.Maths has a median score of \(78\) and a range of \(10\) so all the results were close to the mean and the median. In summary, both English and Maths have a mean score of \(78\) however English has a median score of \(71\) and a range of \(35\) as some students scored much higher than others. This is far greater than the range of scores in the Maths which is \(10\). The range of scores in English is \(35\). The range is not an average, but a measure of the spread of the values (or marks in this case). However, in order to highlight the differences in the marks scored and to give maximum information, a combination of the median and the range would be best. The mean is usually the best measure of the average, as it takes into account all of the data values. It depends on the context in which the result is to be used. The modal score for each subject \(96\) and \(78\) suggests that the students did better in English however this is only considering the two top marks in English and you have no information about the scores of the other students. The median is only a measure of the middle value, as there will be the same number of values above and below this middle value. This is partly true, but there are also some much higher scores. The medians, \(73\) and \(78\) suggest that the students generally scored less well in English. However, looking at the actual scores, you can see that this is not the case. This suggests that the scores of the students are similar in English and Maths. The mean score in each subject is \(78\).
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