College Math

College Math Study Guide

5.8 Median The second measure is median . In order to find the median value, arrange all the values in an order and then select the middle number. In the case where there are two middle values (possible when the number of observations is even), then the median value would be the mean of the two numbers. The value of median is not influenced by any extreme value or outliers in the data set. Let us turn to an example to understand it better. Suppose a series of distribution has the following values: 67, 68, 65, 62, 63, 64, 69, 69, 70, 63. The median of the distribution can be computed by firstly arranging the values in order: 62, 63, 63, 64, 65, 67, 68, 69, 69, 70 Now, since the number of observations is even (10), then the value of median would be mean of the two middle numbers, that are 5 th and 6 th : Median = (65+67)/2 = 66 5.9 Mode The third measure is known as mode . Mode is the value which appears the maximum number of times in the series of values. Suppose a series of distribution has the following values: 67, 68, 65, 62, 63, 64, 69, 69, 70, 69. The modal value will be the value appearing the maximum number of times. In this case, all the observations appear once except 69, which appears three times. Hence, the mode is 69. Finally, range is used to find the spread of the distribution and is calculated by finding the difference between the largest and smallest number in the distribution. 5.10 Standard Deviation and Variance Standard deviation is a measure of dispersion that explains the difference of the number from the mean in a distribution. The higher the standard deviation means the numbers in the series vary largely with respect to the mean value.

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