Which of the following Measure of Averages is not based on all the values given in the data set___________a)Arithmetic Meanb)Geometric Meanc)Mediand)ModeCorrect answer is option 'C'. Can you explain this answer?

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Which of the following Measure of Averages is not based on all the values given in the data set___________

a)
Arithmetic Mean
b)
Geometric Mean
c)
Median
d)
Mode

Correct answer is option 'C'. Can you explain this answer?

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Most Upvoted Answer

Which of the following Measure of Averages is not based on all the val...

The mode is the value or values that occur most frequently in the data set. It represents the most common observation(s) or the peak of the distribution.

Unlike the arithmetic mean, geometric mean, and median, the mode does not take into account all the values in the data set. Instead, it focuses solely on identifying the value(s) with the highest frequency.

For example, consider the following data set: 2, 4, 4, 6, 6, 6, 8, 8, 8. In this case, the mode is 6 because it occurs three times, which is more frequently than any other value. The mode is determined by counting the occurrences of each value, rather than considering the entire range of values.

On the other hand:

The arithmetic mean is calculated by summing all the values in the data set and dividing by the total number of values. It incorporates all the values in the calculation.
The geometric mean is calculated by taking the nth root of the product of n values. It also considers all the values in the data set.
The median represents the middle value when the data set is arranged in ascending or descending order. It includes all the values and identifies the middle observation(s).

Therefore, among the options given, the measure of average that is not based on all the values given in the data set is the mode. It focuses on identifying the most frequently occurring value(s) rather than considering all the values in the data set.

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Which of the following Measure of Averages is not based on all the val...

Median

The median is not based on all the values given in the data set. It is the middle value when the data set is arranged in numerical order. If there is an odd number of values, the median is simply the middle number. If there is an even number of values, the median is the average of the two middle numbers.

Arithmetic Mean, Geometric Mean, and Mode

- The arithmetic mean is calculated by adding up all the values in the data set and dividing by the total number of values.
- The geometric mean is calculated by multiplying all the values in the data set and then taking the nth root, where n is the total number of values.
- The mode is the value that appears most frequently in the data set.

Importance of Median

The median is an important measure of average because it is not affected by extreme values or outliers in the data set. This makes it a more robust measure of central tendency in situations where the data may be skewed or have extreme values.

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