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Which of the following Measure of averages is affected by extreme (very small or very large) values in the data set?
- a)Geometric Mean
- b)Median
- c)Arithmetic Mean
- d)Harmonic Mean
Correct answer is option 'C'. Can you explain this answer?
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Which of the following Measure of averages is affected by extreme (ver...
The arithmetic mean, also known as the mean, is calculated by summing all the values in the data set and dividing by the total number of values. It represents the balance point or center of the data.
Extreme values in the data set can have a significant impact on the arithmetic mean because they contribute to the overall sum. If there are extreme values that are very small or very large, they can pull the mean towards those extreme values.
For example, consider the following data set: 1, 2, 3, 4, 1000. The arithmetic mean of this data set is (1 + 2 + 3 + 4 + 1000) / 5 = 202. If we remove the extreme value of 1000, the mean becomes (1 + 2 + 3 + 4) / 4 = 2.5. The presence of the extreme value significantly affects the arithmetic mean.
On the other hand, the geometric mean, median, and harmonic mean are less influenced by extreme values.
- The geometric mean is calculated by taking the nth root of the product of n values. Since extreme values contribute to the product rather than the sum, their effect is mitigated.
- The median represents the middle value when the data set is arranged in ascending or descending order. Extreme values do not impact the position of the middle value, making the median less affected by them.
- The harmonic mean is calculated by taking the reciprocal of each value, finding their arithmetic mean, and then taking the reciprocal of that result. Extreme values have a smaller influence on the harmonic mean due to the reciprocal operations involved.
In summary, the measure of average that is affected by extreme values in the data set is the arithmetic mean. Extreme values can significantly alter the mean due to their contribution to the overall sum.
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Which of the following Measure of averages is affected by extreme (very small or very large) values in the data set?a)Geometric Meanb)Medianc)Arithmetic Meand)Harmonic MeanCorrect answer is option 'C'. Can you explain this answer?
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