The range of the attendance is given as: 11193.
In statistics, the range of a data set is the difference between the greatest and lowest values. While range has many definitions in various fields of statistics and mathematics, this is the most fundamental definition and is what the given calculator uses. Continuing with the same example:
Arranged in ascending order, the values are:
178,
246,
222,
567,
1200,
5560,
11371,
The highest thus, is: 11,371, while the lowest is 178. Hence, the range is
Range = 11,371 - 178
Range = 11,193
Because it is influenced by outliers, the RANGE is a poor measure of dispersion.
It just takes the two most extreme values from a dataset. It is wasteful of resources to utilize the two extreme values in a dataset since all values in between the maximum and lowest are ignored.
The standard deviation (σ) is given as = 3939.9139170126
Recall that the formula for Standard Deviation is given as:
[tex]s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} .[/tex]
s² = [Σ(xi - μ)²]/N
s² = [(178 - 2763.4285714286)² + ... + (11371 - 2763.4285714286)²]/7
s² = 108660451.71429/7
s² = 15522921.673469
s = √15522921.673469
= 3939.9139170126
When the Range is zero, this indicates that every data point equals the mean.
Together with the previous result, we may conclude that the sample standard deviation of a data set is zero if and only if all of its values are equal.
Learn more about range:
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