# TI-Lists/Mathematical List Functions

There are several kinds of functions that use or create lists. These functions are found in the LIST menus. The LIST menus are accessed by the 2nd function of the STAT key. It is just below the DEL key. There are a variety of mathematical operations that can be done on lists. These are found in the LIST MATH menu. These functions result in a single number answer.

### min( and max(Edit

The minimum function (**2nd LIST MATH 1**) results in the smallest number in the list. The maximum function (**2nd LIST MATH 2**) gives the largest number in the list.

- {4,7,2,5} STO> L1
- {4 7 2 5}

- min(L1)
- 2

- max(L1)
- 7

- min({-3,-8,-1,-4})
- -8

- max({-3,-8,-1,-4})
- -1

### mean(Edit

The averaging function (**2nd LIST MATH 3**) calculates the arithmetic mean of the numbers in the list by adding them up and dividing by the number of items added.

- {2,3,5,6,14} STO> L1
- {2 3 5 6 14}

- mean(L1)
- 6

- mean({40,23,64,14,51})
- 38.4

### median(Edit

The median function (**2nd LIST MATH 4**) finds an average in a different way from the mean. If the list of numbers were listed in order from smallest to largest, the median is the middle number.

- {2,3,5,6,14} STO> L1
- {2 3 5 6 14}

- median(L1)
- 5

- median({40,23,64,14,51})
- 40

If there are an even number of numbers, there is no single middle number. The median in this case if the mean of the two middle numbers. (Add them and divide by 2.)

- median({1.3,1.8,1.1,1.6})
- 1.45

The result, 1.45, is half way between 1.3 and 1.6.

### sum( and prod(Edit

The sum function (**2nd LIST MATH 5**) adds up all the items in a list. The product function (**2nd LIST MATH 6**) multiplies all the items in a list together.

- sum({3,5,6})
- 14

- prod({3,5,6})
- 90

- sum({-4,-2,5,10})
- 9

- prod({-4,-2,5,10})
- 400

- prod({4,3,2,1,0,-1})
- 0

### stdDev( and variance(Edit

The standard deviation function (**2nd LIST MATH 7**) and the variance function (**2nd LIST MATH 8**) give the results of their statistical calulations.

- stdDev({4,5,6,8,11})
- 2.77

- variance({4,5,6,8,11})
- 7.7