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Why use harmonic mean instead of arithmetic mean?
The arithmetic mean is appropriate if the values have the same units, whereas the geometric mean is appropriate if the values have differing units. The harmonic mean is appropriate if the data values are ratios of two variables with different measures, called rates.
Why would you use weighted mean instead of arithmetic mean?
In calculating a simple average, or arithmetic mean, all numbers are treated equally and assigned equal weight. But a weighted average assigns weights that determine in advance the relative importance of each data point. A weighted average is most often computed to equalize the frequency of the values in a data set.
What is the difference between arithmetic mean and weighted mean?
In a simple arithmetic mean, you just add up all the values and divide by the number of data points. In a weighted mean, you multiply the values by a certain factor that is based on some other criterion to give more ‘weight’ to some values than others.
Why harmonic mean is used?
The harmonic mean helps to find multiplicative or divisor relationships between fractions without worrying about common denominators. Harmonic means are often used in averaging things like rates (e.g., the average travel speed given a duration of several trips).
Which mean is most affected by extreme values?
Arithmetic mean
Arithmetic mean is most affected by extreme (minimum and maximum) items of the data.
Why harmonic mean is calculated?
The harmonic mean helps to find multiplicative or divisor relationships between fractions without worrying about common denominators. The weighted harmonic mean is used in finance to average multiples like the price-earnings ratio because it gives equal weight to each data point.
When to use geometric mean or harmonic mean?
1 To average ratios on different scales: use the geometric mean (or arithmetic mean over normalized scores) 2 To average compound rate changes over consistent periods: use the geometric mean 3 To average rates over different periods or lengths: use the harmonic mean (or weighted arithmetic mean)
When is the average speed the harmonic mean?
The same principle applies to more than two segments: given a series of sub-trips at different speeds, if each sub-trip covers the same distance, then the average speed is the harmonic mean of all the sub-trip speeds; and if each sub-trip takes the same amount of time, then the average speed is the arithmetic mean of all the sub-trip speeds.
Which is the weighted arithmetic mean of speeds?
The time fractions are dimensionless (T/T) and are giving the proportion of time spent at the speed of the iᵗʰ driver. It is a weighted arithmetic mean of speeds, weighted by time! And if the time spent at each speed is equal, then it is the arithmetic mean of speeds.
Which is the harmonic mean of A and B?
To start with, here is a geometric construction of the three different means of a and b, where AO is the arithmetic mean (in red), HD is the harmonic mean (in green) and HG is the geometric one (in blue).* Use the harmonic mean when your sample contains fractions and/or extreme values (either too big or too small).