What Is And How To Calculate The Coefficient Of Variation Using The Formula In Statistics Explained
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4 سال پیش
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In this video we discuss
In this video we discuss what is, and how to calculate the coefficient of variation, using the statistics formula, which gives us a process to compare standard deviations of different types of variables.
Transcript/notes
Coefficient of variation
In an earlier video, we compared 2 wide receivers statistics for yards per game for the 2018 season, and we saw that wide out 1 had a better mean, but wide out 2 had a lower standard deviation, meaning that he was a bit more consistent in being closer to his mean.
Because the units of measure, yards per game, were the same, we could compare their standard deviations directly.
But there is a way to compare the standard deviations of two different variables with different units of measurement, by using the coefficient of variation. Here are the formulas for the coefficient of variation for a sample and a population. For a sample it is cvar equals s, the standard deviation over x bar, the mean, times 100, to give a percentage.
And for a population it is cvar equals sigma, the standard deviation over mew, the mean, times 100.
So let’s say that you wanted to compare the consistency of 2 athletes for their 2019 seasons. Wide receiver Michael Thomas and baseball star Yoan Moncada. Yards per game vs hits per game. So we go through the calculations and see that Thomas has an average of 107.8 yards per game with a standard deviation of 38.79. Moncada averages 1.2 hits per game with a standard deviation of 0.98.
So, which player, based on these statistics is more consistent? Using our formula, we plug in Thomas’s numbers, 38.79 standard deviation over a 107.8 mean, times 100 gives us 35.98% for his coefficient of variation. And for Moncada we have a standard deviation of 0.98 divided by a mean of 1.2, times 100, gives us 79.97 percent for his coefficient of variation.
Since Moncada’s coefficient of variation is larger, his data is more variable than Thomas’s. So I would say that Thomas is more consistent based on this data.
Timestamps
0:00 Mean Vs Standard Deviation
0:19 Coefficient Of Variation Explained
0:28 Formulas For Coefficient Of Variation
0:47 Example Problem
1:45 How To Interpret The Coefficient Of Variation
Transcript/notes
Coefficient of variation
In an earlier video, we compared 2 wide receivers statistics for yards per game for the 2018 season, and we saw that wide out 1 had a better mean, but wide out 2 had a lower standard deviation, meaning that he was a bit more consistent in being closer to his mean.
Because the units of measure, yards per game, were the same, we could compare their standard deviations directly.
But there is a way to compare the standard deviations of two different variables with different units of measurement, by using the coefficient of variation. Here are the formulas for the coefficient of variation for a sample and a population. For a sample it is cvar equals s, the standard deviation over x bar, the mean, times 100, to give a percentage.
And for a population it is cvar equals sigma, the standard deviation over mew, the mean, times 100.
So let’s say that you wanted to compare the consistency of 2 athletes for their 2019 seasons. Wide receiver Michael Thomas and baseball star Yoan Moncada. Yards per game vs hits per game. So we go through the calculations and see that Thomas has an average of 107.8 yards per game with a standard deviation of 38.79. Moncada averages 1.2 hits per game with a standard deviation of 0.98.
So, which player, based on these statistics is more consistent? Using our formula, we plug in Thomas’s numbers, 38.79 standard deviation over a 107.8 mean, times 100 gives us 35.98% for his coefficient of variation. And for Moncada we have a standard deviation of 0.98 divided by a mean of 1.2, times 100, gives us 79.97 percent for his coefficient of variation.
Since Moncada’s coefficient of variation is larger, his data is more variable than Thomas’s. So I would say that Thomas is more consistent based on this data.
Timestamps
0:00 Mean Vs Standard Deviation
0:19 Coefficient Of Variation Explained
0:28 Formulas For Coefficient Of Variation
0:47 Example Problem
1:45 How To Interpret The Coefficient Of Variation
4 سال پیش
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