Finds the mean (the average) of a list.

mean(*list*,[*freqlist*])

Press:

- 2ND LIST to enter the LIST menu.
- LEFT to enter the MATH submenu.
- 3 to select mean(, or use arrows.

TI-83/84/+/SE

1 byte

The mean( command finds the mean, or the average, of a list. It's pretty elementary. It takes a list of real numbers as a parameter. For example:

```
:Prompt L1
:Disp "MEAN OF L1",mean(L1
```

That's not all, however. Awesome as the mean( command is, it can also take a frequency list argument, for situations when your elements occur more than once. For example:

`:Disp mean({1,2,3},{5,4,4})`

is short for

`:mean({1,1,1,1,1,2,2,2,2,3,3,3,3})`

The frequency list {5,4,4} means that the first element, 1, occurs 5 times, the second element, 2, occurs 4 times, and the third element, 3, occurs 4 times.

# Advanced Uses

You can also use the frequency list version of mean( to calculate weighted averages. For example, suppose you're trying to average grades in a class where homework is worth 50%, quizzes 20%, and tests 30%. You have a 90% average on homework, 75% on quizzes (didn't study too well), but 95% average on tests. You can now calculate your grade with the mean( command:

`:mean({90,75,95},{50,20,30`

You should get a 88.5 if you did everything right.

Frequency lists don't need to be whole numbers. Amazing as that may sound, your calculator can handle being told that one element of the list occurs 1/3 of a time, and another occurs 22.7 times. It can even handle a frequency of 0 - it will just ignore that element, as though it weren't there. In particular, mean(L1,L2) is effectively equivalent to sum (L1*L2)/sum(L2).

One caveat, though - if all of the elements occur 0 times, there's nothing to take an average of and your calculator will throw an error.

# Error Conditions

**ERR:DATA TYPE**is thrown, among other cases, if the data list is complex, or if the frequencies are not all positive and real.**ERR:DIM MISMATCH**is thrown if the frequency list and the data list have a different number of elements.**ERR:DIVIDE BY 0**is thrown if the frequency list's elements are all 0.

# Related Commands

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