True or false:
The distribution with the largest range necessarily has the largest standard deviation.
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.
Thanks, Bob. The explanation helps!
true
False.
To determine whether this statement is true or false, we need to understand the concepts of range and standard deviation.
The range of a distribution is simply the difference between the maximum and minimum values in that distribution. It tells us how spread out the data is.
On the other hand, the standard deviation is a measure of the average distance between each data point in a distribution and the mean of that distribution. It is a measure of the variability or dispersion of the data.
While the range provides information about the overall spread of the data, the standard deviation considers the spread of each individual data point around the mean. These concepts are related, but they are not directly proportional.
Therefore, the statement is false. It is possible for a distribution with a smaller range to have a larger standard deviation if there is more variation or dispersion between the data points. Similarly, a distribution with a larger range may have a smaller standard deviation if the data points are closer to the mean and have less variation.