why is standard deviation a better measure of variation than the range? Watch

Anjna
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anybody know why
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Mocking_bird
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(Original post by Anjna)
anybody know why
Range gives an overall spread of data from lowest to highest of data and can be influenced by anomolies.
Whereas standard deviation takes into account the variable data/spread about the mean and allows for statistical use so inferences can be made.
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Anjna
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(Original post by Mocking_bird)
Range gives an overall spread of data from lowest to highest of data and can be influenced by anomolies.
Whereas standard deviation takes into account the variable data/spread about the mean and allows for statistical use so inferences can be made.
thanks!
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Revd. Mike
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Just to further illustrate that, imagine the following two data sets:

1, 10, 10, 10, 10, 10, 10, 10, 10, 10

1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

The range is the same for both of them, the the SD will be very different
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Jake22
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The standard deviation tells you how much, on average things vary from the mean of your population.

The range tells you the difference between the largest and smallest values.

Thus the standard deviation gives you an idea of how much every element of your population varies from the average whereas the range just tells you the maximum variation.
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santoshbansal
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•Variance is directly proportional to square of Standard Deviation(Variance = (σ)2) •Standard deviation has its own advantages over any other measure of spread.•It measures the deviation from the mean, which is a very important statistic (Shows the central tendency).•It squares and makes the negative numbers Positive.•The square of small numbers is smaller (Contraction effect) and large numbers larger. (Expanding effect). So it makes you ignore small deviations and see the larger one clearly!•The square is a nice function.
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santoshbansal
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Variance is directly proportional to square of Standard Deviation(Variance = (σ)2)

Standard deviation has its own advantages over any other measure of spread.

It measures the deviation from the mean, which is a very important statistic (Shows the central tendency).

It squares and makes the negative numbers Positive.

The square of small numbers is smaller (Contraction effect) and large numbers larger. (Expanding effect). So it makes you ignore small deviations and see the larger one clearly!

The square is a nice function.
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