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# Beginners statistics: minimum

On this page: Example, with R,  Definition and Use,  Simple formula,  Tips and Notes,  Test yourself,  References  Download R  R is Free, very powerful, and does the boring calculations & graphs for scientists.

### Example, with R

Sometimes a minimum is very obvious:
999999   999999   0   999999   999999   999999   999999

Or you could find the minimum with

### Definition and Use

• The minimum is the lowest number in a list of numbers - if any are negative, it is the largest negative number.
• The minimum is the lowest ranking item in a list - assuming items of equal value are ranked equally.

### Simple formula

Assuming there are n different items in y, and r is their rank:

the minimum of y is y[r = 1]

### Tips and Notes

• If the items' values are nominal, their rank is arbitrary and the minimum is equally arbitrary, misleading, or meaningless.
• If one or more items cannot be ranked, a minimum cannot be found unless those items are excluded - or their rank is provided.
• More than one item may share the minimum value. But if every item is identical the minimum is rather meaningless: their minimum, average and maximum are identical.
• If you are using the minimum in a sample to estimate the minimum in a population, you will always overestimate the population minimum.

### Test yourself

1. You can find the minimum by examining each item in turn,
2. or sort them into ascending order and select the first item,
3. or select the lowest ranking item(s)...

To obtain the minimum of a non-numerical list you must be able to rank its contents:

### Useful references

Wikipedia: Sample maximum and minimum. Full text