A good hash function will yield evenly dispersed outputs. For example, regardless of the hash value, any output is just as likely to occur as any other output. More specifically, if the output range is between 0 and 9, looking at actual outputs, there are just as many 0 values as 1, 2, 3 ... 9 values. Figure 6-7 shows a histogram depicting this near-perfect result.

Figure 6-7. When given random numbers as hash value inputs, even a simple modulus hash function will provide an even distribution of outputs.

Given 1,000 random numbers between 0 and 1,000, the modulus hash function does in fact produce the histogram shown in Figure 6-7. But suppose the situation is not quite so random. Suppose the first 500 numbers are from 0 to 5 and the remaining 500 are between 0 and 1,000. Using the same modulus 10 hash function, the result is the histogram shown in Figure 6-8. This is unfortunate, because clearly the hash function does not return evenly dispersed numbers.