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Unformatted text preview: ed on all items 3. It is very suitable for averaging ratios, rates and percentages 4. It is capable of further mathematical treatment. 5. Unlike AM, it is not affected much by the presence of extreme values Demerits of Geometric mean: 1. It cannot be used when the values are negative or if any of the observations is zero 2. It is difficult to calculate particularly when the items are very large or when there is a frequency distribution. 104 3. It brings out the property of the ratio of the change and not the absolute difference of change as the case in arithmetic mean. 4. The GM may not be the actual value of the series. Combined mean : If the arithmetic averages and the number of items in two or more related groups are known, the combined or the composite mean of the entire group can be obtained by n1 x1 + n 2 x 2 Combined mean X = n1 + n 2 The advantage of combined arithmetic mean is that, we can determine the over, all mean of the combined data without going back to the original data. Example 10: Find the combined mean for the data given below n1 = 20 , x1 = 4 , n2 = 30, x2 = 3 Solution: n1 x1 + n 2 x 2 Combined mean X = n1 + n 2 20 × 4 + 30 × 3 = 20 + 30 80 + 90 = 50 170 = = 3.4 50 Positional Averages: These averages are based on the position of the given observation in a series, arranged in an ascending or descending order. The magnitude or the size of the values does matter as was in the case of arithmetic mean. It is because of the basic difference 105 that the median and mode are called the positional measures of an average. Median : The median is that value of the variate which divides the group into two equal parts, one part comprising all values greater, and the other, all values less than median. Ungrouped or Raw data : Arrange the given values in the increasing or decreasing order. If the number of values are odd, median is the middle value .If the number of values are even, median is the mean of middle two values. By formula n + 1 th Median = Md = item. 2 Example 11: When odd numb...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.

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