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Unformatted text preview: 10-20 20-30 30-40 40-50 50-60 interval Frequency 5 8 12 7 5 3 132 ∴ M0 = 20 + Solution: HISTOGRAM 14 12 Frequency 10 8 6 4 2 0 10 20 Mode 30 40 50 60 Class Interval Daily Wages (in Rs.) Merits of Mode: 1. It is easy to calculate and in some cases it can be located mere inspection 2. Mode is not at all affected by extreme values. 3. It can be calculated for open-end classes. 4. It is usually an actual value of an important part of the series. 5. In some circumstances it is the best representative of data. Demerits of mode: 1. It is not based on all observations. 2. It is not capable of further mathematical treatment. 3. Mode is ill-defined generally, it is not possible to find mode in some cases. 133 4. As compared with mean, mode is affected to a great extent, by sampling fluctuations. 5. It is unsuitable in cases where relative importance of items has to be considered. EMPIRICAL RELATIONSHIP BETWEEN AVERAGES In a symmetrical distribution the three simple averages mean = median = mode. For a moderately asymmetrical distribution, the relationship between them are brought by Prof. Karl Pearson as mode = 3median - 2mean. Example 34: If the mean and median of a moderately asymmetrical series are 26.8 and 27.9 respectively, what would be its most probable mode? Solution: Using the empirical formula Mode = 3 median − 2 mean = 3 × 27.9 − 2 × 26.8 = 30.1 Example 35: In a moderately asymmetrical distribution the values of mode and mean are 32.1 and 35.4 respectively. Find the median value. Solution: Using empirical Formula 1 Median = [2mean+mode] 3 1 = [2 × 35.4 + 32.1] 3 = 34.3 Exercise - 6 I Choose the correct answer: 1. Which of the following represents median? a) First Quartile b) Fiftieth Percentile c) Sixth decile d) Third quartile 134 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. If the grouped data has open-end classes, one can not calculate. a)median b) mode c) mean d) quartile 1 4 Geometric mean of two numbers and is 16 25 1 1 a) b) c) 10 d) 100 10 100 In a symmetric distr...
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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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