Final answer:
The range of a data set is found by subtracting the smallest value from the largest, reflecting data variability. Adjustments can be made to include all values in histograms. Bin size is determined by dividing the adjusted range by the number of desired bins.
Step-by-step explanation:
How to Compute the Range in a Set of Data
To calculate the range of a set of data, you need to identify the smallest and largest numbers in the dataset. The range is simply the difference between these two values. This reflects the spread or variability of the data. For example, if the smallest data value is 1 and the largest is 6, then you would calculate the range by subtracting the smallest value from the largest (6 - 1), which equals 5. This value represents the total span of data in your set.
When determining bin size for a histogram, adjustments can be made to include the maximum and minimum values by slightly extending the range. For instance, by adding and subtracting 0.5 from the minimum and maximum data values (0.5 and 6.5, respectively), we ensure that all data values are accounted for when setting the histogram's intervals. If your set has a small range and you wish to use a fewer number of bins, divide this adjusted range by the desired number of bins to determine the interval size. Using the earlier example with a range of 6 and desiring six bins, you would divide 6 by 6 to get a bin size of 1.
It is essential to consider what is most appropriate and reasonable for your dataset when calculating bin sizes or shape, particularly as they relate to visual representations like histograms.