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Classic Graphing 84 manual · Chapter 12 of 25

Lists

Store data in lists, edit them in the STAT editor, calculate with whole lists and use the LIST menu.

12.1What a list is#

A list is an ordered row of numbers written between curly braces, such as {4, 5, 6}. Six lists are built in: L1 to L6 (2ndL11 to 2ndL66). Lists drive statistics, statistics plots and many tools. You can also make lists with other names.

Example 12.1

Store a list and read an item

  1. Type {1,2,3} with 2nd lparen and 2nd rparen and store it in L1.

    2nd{(1,2,32nd})sto→2ndL11enter

  2. Type L1(3) to read the third item.

    2ndL11(3)enter
Result of the example "Store a list and read an item" The display shows: {1,2,3}→L1 / {1 2 3} / L1(3) / 3.
You should see{1 2 3} L1(3) 3
Example 12.2

Change one item

  1. Store {1,2,3} in L1, then store 9 in the second item.

    2nd{(1,2,32nd})sto→2ndL11enter9sto→2ndL11(2)enter

  2. Show L1.

    2ndL11enter
Result of the example "Change one item" The display shows: {1,2,3}→L1 / {1 2 3} / 9→L1(2) / 9 / L1 / {1 9 3}.
You should see{1 9 3}

12.2Calculate with whole lists#

Arithmetic works on every item at once. A list and a number combine item by item; two lists of the same length combine item by item. Functions such as √( and abs( also work on lists. Lists of different lengths give DIM MISMATCH.

Example 12.3

Double and add one

{1,2,3}×2+1\{1,2,3\}\times2+1

  1. Type {1,2,3}*2+1.

    2nd{(1,2,32nd})×2+1enter
Result of the example "Double and add one" The display shows: {1,2,3}*2+1 / {3 5 7}.
You should see{3 5 7}
Example 12.4

Add two lists

  1. Type {1,2,3}+{10,20,30}.

    2nd{(1,2,32nd})+2nd{(10,20,302nd})enter
Result of the example "Add two lists" The display shows: {1,2,3}+{10,20,30} / {11 22 33}.
You should see{11 22 33}

12.3Enter data in the list editor#

Press stat then 1 (Edit…) to see the lists as columns. Type a value and press enter to store it and move to the next row. Use ◀ and ▶ to change columns and ▲ and ▼ to change rows. At the top of a column, the list name row lets you type a formula for the whole list, or press clear to empty the list.

The STAT menu. The display shows: [EDIT] CALC TESTS / 1:Edit… / 2:SortA( / 3:SortD( / 4:ClrList / 5:SetUpEditor.
The STAT menu.
Example 12.5

Enter three numbers

  1. Press stat, 1, then type 1, 2, 3, pressing enter after each.

    stat11enter2enter3enter
Result of the example "Enter three numbers" The display shows: L1 | L2 | L3 / 1 | | / 2 | | / 3 | | / | | / | | / | | / L1(4)=.
You should seeL1 | L2 | L3 L1(4)=
Example 12.6

Fill two columns

  1. Enter 1, 2 in L1, press right and enter 7, 8 in L2. Then go home and look at L2.

    stat11enter2enter▶7enter8enter2ndQUITmode2ndL22enter
Result of the example "Fill two columns" The display shows: L2 / {7 8}.
You should see{7 8}
Example 12.7

Change an existing value

  1. Enter 1, 2 in L1, press up twice to the first value, press enter to edit, type 9 and enter. Show L1.

    stat11enter2enter▲▲enter9enter2ndQUITmode2ndL11enter
Result of the example "Change an existing value" The display shows: L1 / {9 2}.
You should see{9 2}
Example 12.8

Delete a value

  1. Enter 1, 2, 3, go up to the first value and press del. Show L1.

    stat11enter2enter3enter▲▲▲del2ndQUITmode2ndL11enter
Result of the example "Delete a value" The display shows: L1 / {2 3}.
You should see{2 3}
Example 12.9

Insert a zero

  1. Enter 1, 2, go up to the 1 and press 2nd del (INS). A zero is inserted before it.

    stat11enter2enter▲2ndINSdel2ndQUITmode2ndL11enter
Result of the example "Insert a zero" The display shows: L1 / {1 0 2}.
You should see{1 0 2}
Example 12.10

Type a formula for a whole list

L1={1,2,3}×2L_1=\{1,2,3\}\times2

  1. In the editor press up to the list name row, press enter, type {1,2,3}*2 and press enter.

    stat1▲enter2nd{(1,2,32nd})×2enter2ndQUITmode2ndL11enter
Result of the example "Type a formula for a whole list" The display shows: L1 / {2 4 6}.
You should see{2 4 6}
Example 12.11

Empty a list from the editor

  1. Enter 1, 2 in L1, go up to the list name and press clear, then check the length with dim(L1).

    stat11enter2enter▲▲▲clear2ndQUITmode2ndLISTstat▶32ndL11)enter
Result of the example "Empty a list from the editor" The display shows: dim(L1) / 0.
You should see0

12.4The LIST menu#

Press 2ndLISTstat. The tabs are NAMES, OPS and MATH; use ◀ and ▶ to switch.

The OPS tab of the LIST menu. The display shows: NAMES [OPS] MATH / 1:SortA( / 2:SortD( / 3:dim( / 4:Fill( / 5:seq( / 6:cumSum( / 7↓ΔList(.
The OPS tab of the LIST menu.
TabItems
NAMES1 to 6: L1 to L6
OPS1 SortA(, 2 SortD(, 3 dim(, 4 Fill(, 5 seq(, 6 cumSum(, 7 ΔList(, 9 augment(, 0 List►matr(, A Matr►list(
MATH1 min(, 2 max(, 3 mean(, 4 median(, 5 sum(, 6 prod(, 7 stdDev(, 8 variance(

12.5Sort a list#

Example 12.12

Sort ascending

  1. Store {3,1,2} in L1.

    2nd{(3,1,22nd})sto→2ndL11enter

  2. Press 2nd stat, right, 1 (SortA(), type L1 and a bracket.

    2ndLISTstat▶12ndL11)enter

  3. Show L1.

    2ndL11enter
Result of the example "Sort ascending" The display shows: {3,1,2}→L1 / {3 1 2} / SortA(L1) / Done / L1 / {1 2 3}.
You should see{1 2 3}
Example 12.13

Sort descending

  1. Store {3,1,2} in L1 and use SortD( (OPS item 2).

    2nd{(3,1,22nd})sto→2ndL11enter2ndLISTstat▶22ndL11)enter2ndL11enter
Result of the example "Sort descending" The display shows: {3,1,2}→L1 / {3 1 2} / SortD(L1) / Done / L1 / {3 2 1}.
You should see{3 2 1}

12.6Build lists: seq, cumSum, ΔList, Fill, augment, dim#

seq(X2,X,1,4)={1,4,9,16}\texttt{seq(}X^2,X,1,4\texttt{)}=\{1,4,9,16\}
seq( builds a list from a rule: expression, variable, start, end.
Example 12.14

Squares with seq(

  1. Press 2nd stat, right, 5 (seq(), then X², X, 1, 4 and a bracket.

    2ndLISTstat▶5X,T,θ,nx²,X,T,θ,n,1,4)enter
Result of the example "Squares with seq(" The display shows: seq(X²,X,1,4) / {1 4 9 16}.
You should see{1 4 9 16}
Example 12.15

Running totals

  1. cumSum( is OPS item 6.

    2ndLISTstat▶62nd{(1,2,32nd}))enter
Result of the example "Running totals" The display shows: cumSum({1,2,3}) / {1 3 6}.
You should see{1 3 6}
Example 12.16

Differences between neighbours

  1. ΔList( is OPS item 7.

    2ndLISTstat▶72nd{(1,4,92nd}))enter
Result of the example "Differences between neighbours" The display shows: ΔList({1,4,9}) / {3 5}.
You should see{3 5}
Example 12.17

Join two lists

  1. augment( is OPS item 9.

    2ndLISTstat▶92nd{(12nd}),2nd{(22nd}))enter
Result of the example "Join two lists" The display shows: augment({1},{2}) / {1 2}.
You should see{1 2}
Example 12.18

Length of a list

  1. dim( is OPS item 3.

    2ndLISTstat▶32nd{(5,6,72nd}))enter
Result of the example "Length of a list" The display shows: dim({5,6,7}) / 3.
You should see3
Example 12.19

Fill a list with one value

  1. Store {1,2,3} in L2, then use Fill( (OPS item 4) with 7 and L2.

    2nd{(1,2,32nd})sto→2ndL22enter2ndLISTstat▶47,2ndL22)enter

  2. Show L2.

    2ndL22enter
Result of the example "Fill a list with one value" The display shows: {1,2,3}→L2 / {1 2 3} / Fill(7,L2) / Done / L2 / {7 7 7}.
You should see{7 7 7}
Example 12.20

Clear a list (ClrList)

  1. Store {1} in L1. Press stat, 4 (ClrList), type L1 and press enter.

    2nd{(12nd})sto→2ndL11enterstat42ndL11enter

  2. Check dim(L1).

    2ndLISTstat▶32ndL11)enter
Result of the example "Clear a list (ClrList)" The display shows: {1}→L1 / {1} / ClrList L1 / Done / dim(L1) / 0.
You should see0

12.7Mean, median, sum and other list math#

xˉ=∑xn,sx=∑(x−xˉ)2n−1\bar{x}=\frac{\sum x}{n},\qquad s_x=\sqrt{\frac{\sum (x-\bar{x})^2}{n-1}}
The mean and the sample standard deviation.
Example 12.21

Mean

1+2+3+104=4\frac{1+2+3+10}{4}=4

  1. Press 2nd stat, left (MATH), 3 (mean().

    2ndLISTstat◀32nd{(1,2,3,102nd}))enter
Result of the example "Mean" The display shows: mean({1,2,3,10}) / 4.
You should see4
Example 12.22

Median

  1. Press 2nd stat, left, 4 (median().

    2ndLISTstat◀42nd{(1,2,3,102nd}))enter
Result of the example "Median" The display shows: median({1,2,3,10}) / 2.5.
You should see2.5
Example 12.23

Sum and product

  1. sum( is MATH item 5.

    2ndLISTstat◀52nd{(1,2,3,42nd}))enter

  2. prod( is MATH item 6.

    2ndLISTstat◀62nd{(1,2,3,42nd}))enter
Result of the example "Sum and product" The display shows: sum({1,2,3,4}) / 10 / prod({1,2,3,4}) / 24.
You should see10 24
Example 12.24

Standard deviation

  1. stdDev( is MATH item 7.

    2ndLISTstat◀72nd{(1,2,3,4,52nd}))enter
Result of the example "Standard deviation" The display shows: stdDev({1,2,3,4,5}) / 1.58113883.
You should see1.58113883
Example 12.25

Variance

  1. variance( is MATH item 8.

    2ndLISTstat◀82nd{(1,2,3,4,52nd}))enter
Result of the example "Variance" The display shows: variance({1,2,3,4,5}) / 2.5.
You should see2.5
Example 12.26

Smallest and largest

  1. min( and max( are MATH items 1 and 2.

    2ndLISTstat◀12nd{(4,9,22nd}))enter2ndLISTstat◀22nd{(4,9,22nd}))enter
Result of the example "Smallest and largest" The display shows: min({4,9,2}) / 2 / max({4,9,2}) / 9.
You should seemin({4,9,2}) 2 max({4,9,2}) 9

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