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Which of the following is the most unstable average?
- a)Median
- b)Arithmetic mean
- c)Mode
- d)Geometric mean
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Which of the following is the most unstable average?a)Medianb)Arithmet...
- Mode: The word mode has been derived from the French word “la Mode” which signifies the most fashionable values of distribution because it is repeated the highest number of times in the series. The mode is the most frequently observed data value. It is denoted by Mo.
- The mode is seldom used and its computation is easy, but it is highly unstable and may change with minor shifts in the frequencies from one interval to another.
- However, there are situations in which the only mode can be used.
- For example, if a shoe company wants to how which size of shoe it should produce more, it would use mode as a measure of central tendency. The most frequently sold size of the shoes is the mode.
- Arithmetic mean: The arithmetic mean is the most commonly used measure of central tendency. The mean represents the central tendency. It is defined as the sum of the values of all observations divided by the number of observations and is usually denoted by X. In general, if there are N observations as X1, X2, X3, ..., XN, then the Arithmetic Mean is given by
This will be written in simpler form without the index i.
Thus mean = N ∑ X/N where, ΣX = sum of all observations and N = total number of observations. - Median is that positional value of the variable which divides the distribution into two equal parts, one part comprises all values greater than or equal to the median value and the other comprises all values less than or equal to it. The Median is the “middle” element when the data set is arranged in order of the magnitude. Since the median is determined by the position of different values, it remains unaffected if, say, the size of the largest value increases. The median can be easily computed by sorting the data from smallest to largest and finding out the middle value.
Hence, we conclude that Mode is the most unstable average.
Most Upvoted Answer
Which of the following is the most unstable average?a)Medianb)Arithmet...
- Mode: The word mode has been derived from the French word “la Mode” which signifies the most fashionable values of distribution because it is repeated the highest number of times in the series. The mode is the most frequently observed data value. It is denoted by Mo.
- The mode is seldom used and its computation is easy, but it is highly unstable and may change with minor shifts in the frequencies from one interval to another.
- However, there are situations in which the only mode can be used.
- For example, if a shoe company wants to how which size of shoe it should produce more, it would use mode as a measure of central tendency. The most frequently sold size of the shoes is the mode.
- Arithmetic mean: The arithmetic mean is the most commonly used measure of central tendency. The mean represents the central tendency. It is defined as the sum of the values of all observations divided by the number of observations and is usually denoted by X. In general, if there are N observations as X1, X2, X3, ..., XN, then the Arithmetic Mean is given by
This will be written in simpler form without the index i.
Thus mean = N ∑ X/N where, ΣX = sum of all observations and N = total number of observations. - Median is that positional value of the variable which divides the distribution into two equal parts, one part comprises all values greater than or equal to the median value and the other comprises all values less than or equal to it. The Median is the “middle” element when the data set is arranged in order of the magnitude. Since the median is determined by the position of different values, it remains unaffected if, say, the size of the largest value increases. The median can be easily computed by sorting the data from smallest to largest and finding out the middle value.
Hence, we conclude that Mode is the most unstable average.
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Community Answer
Which of the following is the most unstable average?a)Medianb)Arithmet...
Explanation:
Definition of the terms:
- Median: The median is the middle value of a set of numbers when they are arranged in order. If the set contains an odd number of values, the median is the middle value. If the set contains an even number of values, the median is the average of the two middle values.
- Arithmetic Mean: The arithmetic mean is the sum of all the values in a set divided by the number of values in the set. It is also known as the average.
- Mode: The mode is the value that appears most frequently in a set of numbers.
- Geometric Mean: The geometric mean is the nth root of the product of n numbers.
Unstable Average:
- An unstable average is one that can be easily influenced or skewed by extreme values in the dataset. If the addition or removal of an extreme value significantly changes the average, it is considered unstable.
Explanation of options:
a) Median:
- The median is not affected by extreme values in the dataset. It only depends on the position of the values when they are arranged in order. Therefore, it is a stable average.
b) Arithmetic Mean:
- The arithmetic mean is influenced by extreme values in the dataset. Adding or removing an extreme value can significantly change the average. Therefore, it is a relatively stable average compared to the geometric mean.
c) Mode:
- The mode is the value that appears most frequently in a set of numbers. It is not affected by extreme values because it only depends on the frequency of values. However, if there is no value that appears more than once, there is no mode. Therefore, it is also a stable average.
d) Geometric Mean:
- The geometric mean is highly influenced by extreme values in the dataset. It is calculated by taking the nth root of the product of n numbers. If there is a large or small extreme value in the dataset, it will have a significant impact on the geometric mean. Therefore, it is the most unstable average among the given options.
Conclusion:
- The most unstable average among median, arithmetic mean, mode, and geometric mean is the geometric mean. It is highly influenced by extreme values in the dataset and can change significantly when extreme values are added or removed.
Definition of the terms:
- Median: The median is the middle value of a set of numbers when they are arranged in order. If the set contains an odd number of values, the median is the middle value. If the set contains an even number of values, the median is the average of the two middle values.
- Arithmetic Mean: The arithmetic mean is the sum of all the values in a set divided by the number of values in the set. It is also known as the average.
- Mode: The mode is the value that appears most frequently in a set of numbers.
- Geometric Mean: The geometric mean is the nth root of the product of n numbers.
Unstable Average:
- An unstable average is one that can be easily influenced or skewed by extreme values in the dataset. If the addition or removal of an extreme value significantly changes the average, it is considered unstable.
Explanation of options:
a) Median:
- The median is not affected by extreme values in the dataset. It only depends on the position of the values when they are arranged in order. Therefore, it is a stable average.
b) Arithmetic Mean:
- The arithmetic mean is influenced by extreme values in the dataset. Adding or removing an extreme value can significantly change the average. Therefore, it is a relatively stable average compared to the geometric mean.
c) Mode:
- The mode is the value that appears most frequently in a set of numbers. It is not affected by extreme values because it only depends on the frequency of values. However, if there is no value that appears more than once, there is no mode. Therefore, it is also a stable average.
d) Geometric Mean:
- The geometric mean is highly influenced by extreme values in the dataset. It is calculated by taking the nth root of the product of n numbers. If there is a large or small extreme value in the dataset, it will have a significant impact on the geometric mean. Therefore, it is the most unstable average among the given options.
Conclusion:
- The most unstable average among median, arithmetic mean, mode, and geometric mean is the geometric mean. It is highly influenced by extreme values in the dataset and can change significantly when extreme values are added or removed.
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