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Which mean is most affected by extreme values?
- a)Geometric Mean
- b)Harmonic Mean
- c)Arithmetic mean
- d)Trimmed Mean
Correct answer is option 'C'. Can you explain this answer?
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Which mean is most affected by extreme values?a)Geometric Meanb)Harmon...
Arithmetic Mean is most affected by extreme values
Arithmetic Mean is the sum of all values in a dataset divided by the number of values. Extreme values can significantly impact the arithmetic mean because they have a disproportionate effect on the total sum.
Extreme values can skew the arithmetic mean in one direction, pulling it towards the extreme value. This can lead to a misleading representation of the central tendency of the dataset.
Comparing with other means:
- Geometric Mean: Geometric Mean is less affected by extreme values because it involves multiplying all values in the dataset. Extreme values have less impact on the overall product compared to the sum in arithmetic mean.
- Harmonic Mean: Harmonic Mean is also less affected by extreme values as it considers the reciprocal of the values. Extreme values have a balancing effect on the harmonic mean.
- Trimmed Mean: Trimmed Mean is specifically designed to reduce the impact of extreme values. It involves removing a certain percentage of extreme values from both ends of the dataset before calculating the mean.
In conclusion, the Arithmetic Mean is most affected by extreme values compared to other means. It is important to consider the nature of the dataset and the presence of extreme values when choosing the appropriate mean for analysis.
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Which mean is most affected by extreme values?a)Geometric Meanb)Harmon...
The arithmetic mean is the most commonly used measure of central tendency. It is calculated by summing all the values in a dataset and dividing it by the total number of values. The arithmetic mean is sensitive to extreme values because it takes into account the magnitude of each data point.
When there are extreme values in a dataset, they can significantly affect the arithmetic mean. Extreme values have a disproportionate impact on the sum of the values used in the calculation, pulling the mean towards them.
For example, let's consider a dataset representing the incomes of a group of individuals. If there is an outlier with an extremely high income, the arithmetic mean will be greatly influenced by this value. The presence of the extreme value can inflate the arithmetic mean, making it higher than the typical income for the majority of individuals in the dataset.
To address the issue of extreme values affecting the arithmetic mean, alternative measures like trimmed mean or winsorized mean can be used. These methods involve removing or downweighting a certain percentage of extreme values before calculating the mean. This helps mitigate the impact of outliers on the resulting value.
In summary, the arithmetic mean is the measure of central tendency that is most affected by extreme values in a dataset.
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Which mean is most affected by extreme values?a)Geometric Meanb)Harmonic Meanc)Arithmetic meand)Trimmed MeanCorrect answer is option 'C'. Can you explain this answer?
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