Mean
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This document compares and contrasts the arithmetic mean, median, and mode. It outlines the merits and demerits of each measure of central tendency. The arithmetic mean is summarized as the most stable and capable of algebraic treatment, as it uses all observations in its calculation. However, it can be affected by extreme values. The median and mode are not as capable mathematically but are not impacted by outliers in the same way. Overall, the document concludes that the mean is the best average.
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This document discusses measures of central tendency, including the mean, median, and mode. It provides examples of calculating each measure using sample data sets. The mean is the average value calculated by summing all values and dividing by the number of data points. The median is the middle value when data is ordered from lowest to highest. The mode is the most frequently occurring value. Examples are given to demonstrate calculating the mean, median, and mode from sets of numeric data.
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Chapter 2
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Mean
- 1. ARITHMETIC MEAN MERITS Simple to understand. Easy to calculate. Based on all observation. Capable for algebraic treatment. It is more stable. It can be determined in most of the cases. .
- 2. Demerits It is effected by extrme values. Not suitable for ratios and percentages. It cannot be calculated for qualitative data. Misleading and absurd result in some cases. It does not coincide with any observed values
- 3. Compare Mean, Median and Mode Mean is a mathematical average but Median and mode are positional averages. Mean is based on all observation while median is the middle item and mode is commonly found item. Median and mode are values found in the series but not mean.
- 4. •Median and mode can be graphically located but not mean. •Mean is affected by extreme item but not median and mode. •Mean is capable of further mathematical treatment but not median and mode
- 5. MEDIAN MERITS It is very simple measure. Not affected extreme items. It can locate by a mere glance. It can be determined by graphically.
- 6. Demerits Not based on all observation. Not capable of algebraic treatments. It requires arraying also. In the case of continuous series interpolation formula is used.
- 7. MODE MERITS Can be located graphically. It is simple measure of central tendency. Less affected by extreme items It coincide with one of the values of the series.
- 8. Demerits Not base on all observations. Not capable of further algebraic treatment. It is ill-defined in some cases. Sometimes grouping to identify the Modal values.
- 9. BEST AVERAGE : MEAN Easily calculated. Simple to under stand. Capable for algebraic treatment.
- 10. •Based on all observation. •It can located without arranging the data. •It is stable fro sample to sample when sample selected is sufficiently large.