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To find the average speed of a journey which is the appropriate measure of central tendency____________
- a)Mean
- b)Geometric Mean
- c)Harmonic Mean
- d)Weighted Mean
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
To find the average speed of a journey which is the appropriate measur...
The appropriate measure of central tendency to find the average speed of a journey is the Harmonic Mean. Let's understand why the Harmonic Mean is the correct choice.
Mean:
The mean is a measure of central tendency that is commonly used to find the average of a set of values. It is calculated by summing up all the values and dividing by the total number of values. However, the mean is not suitable for finding the average speed of a journey because it does not take into account the distance traveled and the time taken.
Geometric Mean:
The geometric mean is another measure of central tendency that is used when dealing with values that are proportional or in a multiplicative relationship. It is calculated by taking the nth root of the product of n values. However, the geometric mean is not appropriate for finding the average speed of a journey because it does not consider the different distances traveled and the corresponding time taken.
Weighted Mean:
The weighted mean is a measure of central tendency that assigns weights to each value in the set, reflecting their importance or significance. It is calculated by multiplying each value by its corresponding weight, summing up the weighted values, and dividing by the sum of the weights. While the weighted mean can be useful in certain situations, it may not be appropriate for finding the average speed of a journey unless there are specific weights assigned to different distances or time intervals.
Harmonic Mean:
The harmonic mean is a measure of central tendency that is specifically used to find the average of rates or speeds. It is calculated by dividing the total distance traveled by the total time taken. The formula for the harmonic mean is given by:
Harmonic Mean = (Total distance traveled) / (Total time taken)
Since the harmonic mean takes into account both the distance traveled and the time taken, it provides a more accurate measure of the average speed of a journey. By using the harmonic mean, we ensure that each distance and time interval contributes proportionally to the overall average speed.
Therefore, the appropriate measure of central tendency to find the average speed of a journey is the Harmonic Mean.
Mean:
The mean is a measure of central tendency that is commonly used to find the average of a set of values. It is calculated by summing up all the values and dividing by the total number of values. However, the mean is not suitable for finding the average speed of a journey because it does not take into account the distance traveled and the time taken.
Geometric Mean:
The geometric mean is another measure of central tendency that is used when dealing with values that are proportional or in a multiplicative relationship. It is calculated by taking the nth root of the product of n values. However, the geometric mean is not appropriate for finding the average speed of a journey because it does not consider the different distances traveled and the corresponding time taken.
Weighted Mean:
The weighted mean is a measure of central tendency that assigns weights to each value in the set, reflecting their importance or significance. It is calculated by multiplying each value by its corresponding weight, summing up the weighted values, and dividing by the sum of the weights. While the weighted mean can be useful in certain situations, it may not be appropriate for finding the average speed of a journey unless there are specific weights assigned to different distances or time intervals.
Harmonic Mean:
The harmonic mean is a measure of central tendency that is specifically used to find the average of rates or speeds. It is calculated by dividing the total distance traveled by the total time taken. The formula for the harmonic mean is given by:
Harmonic Mean = (Total distance traveled) / (Total time taken)
Since the harmonic mean takes into account both the distance traveled and the time taken, it provides a more accurate measure of the average speed of a journey. By using the harmonic mean, we ensure that each distance and time interval contributes proportionally to the overall average speed.
Therefore, the appropriate measure of central tendency to find the average speed of a journey is the Harmonic Mean.
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To find the average speed of a journey which is the appropriate measur...
The harmonic mean is specifically designed for rates or ratios, making it suitable for calculating average speeds. It is calculated by taking the reciprocal of each value, finding their arithmetic mean, and then taking the reciprocal of that result.
When finding the average speed of a journey, it is common to have different segments or intervals with varying speeds. The harmonic mean is useful in this scenario because it gives more weight to the slower speeds.
The harmonic mean ensures that the calculated average reflects the overall time taken for the journey, considering the different speeds and distances traveled in each segment. By taking the reciprocal of the speeds, finding their arithmetic mean, and then taking the reciprocal again, the harmonic mean effectively balances the impact of different speeds on the average.
On the other hand, the mean, geometric mean, and weighted mean are not as appropriate for finding the average speed of a journey. The mean does not account for the different speeds and distances traveled. The geometric mean is more suitable for multiplicative relationships rather than additive ones like average speeds. The weighted mean involves assigning different weights to each value, which may not be necessary unless there are specific considerations for certain segments of the journey.
Therefore, to find the average speed of a journey, the appropriate measure of central tendency is the harmonic mean. It accounts for the varying speeds and ensures the average reflects the overall time taken for the journey.
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To find the average speed of a journey which is the appropriate measure of central tendency____________a)Meanb)Geometric Meanc)Harmonic Meand)Weighted MeanCorrect answer is option 'C'. Can you explain this answer?
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