11-Unit11

This is tedious when the number of items in a series

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Unformatted text preview: he number of items in a series is numerous. Since the value of median is determined by observation, it is not a true representative of all the values. Median is not amenable to further algebraic treatment. The value of median is affected by sampling fluctuation. Mode Mode is the most repeating value of a distribution. When one item repeats more number of times than other or when two items repeat equal number of times, mode is ill defined. Under such case, mode is calculated by the formula (3 median – 2 mean). Mode is a widely used measure of central tendency in business. We speak of model wage which is the wage earned by most of the workers. Model shoe size is the mostly demanded shoe. Merits of Mode Mode is the most typical and frequented value of the distribution. It is not affected by extreme values. Mode can be determined even for series with open-ended classes. Mode can be graphically determined. Sikkim Manipal University Page No. 181 Research Methodology Unit 11 Demerits of Mode 1. It is difficult to calculate mode when one item repeats more number of times than others. 2. Mode is not capable of further algebraic treatment. 3. Mode is not based on all the items of the series. 4. Mode is not rigidly defined. There are several formulae for calculating mode. Mode for Individual Series 1. Calculation of mode for the following data. 7 10 8 5 8 6 8 9 Since item 8 repeats more number of times. Therefore mode = 8 Calculation of mode when mode is ill defined. 2. Calculation of mode for the following data. 15 25 14 18 21 16 19 20 Since no item repeats more number of times mode is ill defined. Mode = (3 median – 2 mean) Mean = 18.5 Median = (18 +19)/2 = 18.5 = (3 X 18.5) – (2 X 18.5) = 55.5 – 36.5 Mode = 19 Mode for Discrete data Series In discrete series the item with highest frequency is taken as mode. 3. Find mode for the following data. Sikkim Manipal University Page No. 182 Research Methodology Unit 11 Size of shirt No. of persons 28 10 29 20 30 40 31 65 32 50 33 15...
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