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True or false:

The distribution with the largest range necessarily has the largest standard deviation.

  • Stats -

    False. Consider the distriubtion with a mean of 1000, then 10000 data points between 99.9 and 100.1, and a data point at zero, and one at a thousand. Its standard deviation is very small compared to
    a mean of 100, 40 datapoints between 80 and 120, the standard deviation will be larger than the first, even if its range is smaller.

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    Thanks, Bob. The explanation helps!

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