Question
Write the properties Of a good measure Of dispersion. The following information for the two groups of individuals is given as:
Answer :
Word Count : 467
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Alright — let's go step-by-step. --- ## Step 1: Properties of a good measure of dispersion These are standard in statistics: 1. Easy to understand and calculate — Should be simple to compute and interpret. 2. Based on all observations — Uses every data item; not just extremes like range. 3. Not unduly affected by extreme values (for some measures like mean deviation and SD this holds better than range). 4. Rigidly defined — Should have a unique, unambiguous formula. 5. Suitable for further mathematical treatment — e.g., variance is better than mean deviation for algebra. 6. Stability under sampling — Should fluctuate little from sample to sample. 7. Independent of origin but not scale — Adding a constant to all data doesn’t change dispersion; multiplying changes proportionally. --- ## Step 2: Understanding the given data We have two groups: | Group | Size \( n_i \) | Mean \( \bar{x}_i \) | Variance \( s_i^2 \) | |-------|--------------|-------------------|---------------------| | I | 50 | 20 | 4 |
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