Trident Help

Natural Color Graphing manual · Chapter 12 of 18

Statistics: lists and calculations

Enter data in six lists, then get one-variable and two-variable statistics and regression.

12.1Enter data in the list editor#

Press MENU then 2. Six lists, List 1 to List 6, appear as columns. Type a number and press EXE; it is stored and the cursor drops to the next row. Use the arrows to move around. The bottom bar offers GRAPH, CALC, TEST, INTR, DIST and, on page 2 (F6), DEL, DEL-ALL and INS.

Example 12.1

Enter 1, 2, 3

  1. Open Statistics and type three values.

    MENU21EXE2EXE3EXE
    After step 1: Open Statistics and type three values. The display shows: List 1 | List 2 | List 3 | List 4 | List 5 | List 6 / 1 | | | | | / 2 | | | | | / 3 | | | | | / | | | | | / List 1[4]= / GRAPH CALC TEST INTR DIST ▷.
Result of the example "Enter 1, 2, 3" The display shows: List 1 | List 2 | List 3 | List 4 | List 5 | List 6 / 1 | | | | | / 2 | | | | | / 3 | | | | | / | | | | | / List 1[4]= / GRAPH CALC TEST INTR DIST ▷.
You should seeList 1[4]=
Example 12.2

Delete a row

  1. Enter 1, 2, 3, go up twice, then DEL (page 2).

    MENU21EXE2EXE3EXE▲▲F6F1
Result of the example "Delete a row" The display shows: List 1 | List 2 | List 3 | List 4 | List 5 | List 6 / 1 | | | | | / 3 | | | | | / | | | | | / List 1[2]=3 / DEL DEL-ALL INS · · ▷.
You should seeList 1[2]=3
Example 12.3

Insert a row

  1. Enter 1, 2, 3, go up twice, then INS.

    MENU21EXE2EXE3EXE▲▲F6F3
Result of the example "Insert a row" The display shows: List 1 | List 2 | List 3 | List 4 | List 5 | List 6 / 1 | | | | | / 0 | | | | | / 2 | | | | | / 3 | | | | | / | | | | | / List 1[2]=0 / DEL DEL-ALL INS · · ▷.
You should seeList 1[2]=0
Example 12.4

Clear a list

  1. Enter 1, 2, 3, then DEL-ALL.

    MENU21EXE2EXE3EXEF6F2
Result of the example "Clear a list" The display shows: List 1 | List 2 | List 3 | List 4 | List 5 | List 6 / | | | | | / List 1[1]= / DEL DEL-ALL INS · · ▷.
You should seeList 1[1]=
Example 12.5

Lists are shared with Run-Matrix

  1. Enter 1, 2, 3, then in Run-Matrix take the Sum of List 1.

    MENU21EXE2EXE3EXEMENU1OPTNF1F3OPTNF1F11EXE
Result of the example "Lists are shared with Run-Matrix" The display shows: Sum List 1 / 6 / List Dim Sum Mean Med ▷.
You should see6

12.2One-variable statistics#

With data in List 1 press F2 (CALC) then F1 (1-VAR). Scroll with ▼. The results are x̄, Σx, Σx², σx, sx, n, minX, Q1, Med, Q3, maxX.

xˉ=∑xn,σx=∑(x−xˉ)2n,sx=∑(x−xˉ)2n−1\bar x=\frac{\sum x}{n},\qquad \sigma_x=\sqrt{\frac{\sum (x-\bar x)^2}{n}},\qquad s_x=\sqrt{\frac{\sum (x-\bar x)^2}{n-1}}
Mean, population and sample standard deviation
Example 12.6

Mean and spread of 1 to 5

  1. Enter 1 to 5 and choose 1-VAR.

    MENU21EXE2EXE3EXE4EXE5EXEF2F1
    After step 1: Enter 1 to 5 and choose 1-VAR. The display shows: 1-Variable / x̄=3 / Σx=15 / Σx²=55 / σx=1.414213562 / sx=1.58113883.
Result of the example "Mean and spread of 1 to 5" The display shows: 1-Variable / x̄=3 / Σx=15 / Σx²=55 / σx=1.414213562 / sx=1.58113883.
You should see1-Variable x̄=3 Σx=15 Σx²=55 σx=1.414213562 sx=1.58113883
Example 12.7

Quartiles

  1. Scroll down to the end of the list.

    MENU21EXE2EXE3EXE4EXE5EXEF2F1▼▼▼▼▼▼▼▼▼▼▼
Result of the example "Quartiles" The display shows: n=5 / minX=1 / Q1=1.5 / Med=3 / Q3=4.5 / maxX=5.
You should seeQ1=1.5 Med=3 Q3=4.5 maxX=5
Example 12.8

A frequency list

  1. List 1 = 1, 2 and List 2 = 3, 1. In CALC, SET, move to 1Var Freq and choose List 2.

    MENU21EXE2EXE▲▲▶3EXE1EXEF2F4▼2EXEEXITF1
Result of the example "A frequency list" The display shows: 1-Variable / x̄=1.25 / Σx=5 / Σx²=7 / σx=0.4330127019 / sx=0.5.
You should seex̄=1.25 Σx=5

12.3Two-variable statistics#

Put x in List 1 and y in List 2 (type all of List 1, go up to the top, press right, and type List 2). Choose F2 (CALC) then F2 (2-VAR).

Example 12.9

2-VAR results

  1. x = 1, 2, 3 and y = 2, 4, 7.

    MENU21EXE2EXE3EXE▲▲▲▶2EXE4EXE7EXEF2F2▼▼▼▼▼▼▼▼
Result of the example "2-VAR results" The display shows: Σy=13 / Σy²=69 / σy=2.054804668 / sy=2.516611478 / Σxy=31 / minX=1.
You should seeΣxy=31

12.4Regression lines and curves#

With x and y data, press F2 (CALC), then F3 (REG) and pick a model. The fit is shown with its coefficients. F1 (COPY) copies the equation to the function list, and F6 (DRAW) draws the data and the curve.

F keyModelCoefficients shown
F1 then F1 or F2X: ax+b or a+bxa, b, r, r²
F2Med-Med linea, b
F3X² quadratica, b, c, r²
F4X³ cubica, b, c, d
F5X⁴ quartica, b, c, d, e
F6 then F1Loga, b
F6 then F2Exp: ae^bx or ab^xa, b
F6 then F3Powera, b
F6 then F4Sina, b, c, d
F6 then F5Logistica, b, c
y=ax+b,a=SxySxx,b=yˉ−axˉy=ax+b,\qquad a=\frac{S_{xy}}{S_{xx}},\quad b=\bar y-a\bar x
Least-squares line
Example 12.10

A perfect line

  1. x = 1 to 5, y = 3, 5, 7, 9, 11; CALC, REG, X, ax+b.

    MENU21EXE2EXE3EXE4EXE5EXE▲▲▲▲▲▶3EXE5EXE7EXE9EXE11EXEF2F3F1F1
Result of the example "A perfect line" The display shows: LinearReg(ax+b) / a=2 / b=1 / r=1 / r²=1 / MSe=0 / COPY · · · · DRAW.
You should seeLinearReg(ax+b) a=2 b=1 r=1
Example 12.11

Quadratic fit

  1. x = 1 to 4, y = 2, 5, 10, 17; REG, X².

    MENU21EXE2EXE3EXE4EXE▲▲▲▲▶2EXE5EXE10EXE17EXEF2F3F3
Result of the example "Quadratic fit" The display shows: QuadReg / a=1 / b=0 / c=1 / R²=1 / MSe=7.888609052×10^-31 / COPY · · · · DRAW.
You should seea=1 b=0 c=1
Example 12.12

Copy the fit to Y=

  1. Linear fit, then COPY.

    MENU21EXE2EXE3EXE4EXE5EXE▲▲▲▲▲▶3EXE5EXE7EXE9EXE11EXEF2F3F1F1F1
Result of the example "Copy the fit to Y=" The display shows: Copied to Y1 / Y1=2X+1.
You should seeCopied to Y1
Example 12.13

Exponential fit

  1. x = 0 to 3, y = 3, 6, 12, 24; REG, Exp, ab^x.

    MENU20EXE1EXE2EXE3EXE▲▲▲▲▶3EXE6EXE12EXE24EXEF2F3F6F2F2
Result of the example "Exponential fit" The display shows: ExpReg(a·b^x) / a=3 / b=2 / r=1 / r²=1 / COPY · · · · DRAW.
You should seea=3 b=2
Example 12.14

Power fit

  1. x = 1 to 4, y = 2, 16, 54, 128; REG, Power.

    MENU21EXE2EXE3EXE4EXE▲▲▲▲▶2EXE16EXE54EXE128EXEF2F3F6F3
Result of the example "Power fit" The display shows: PowerReg / a=2 / b=3 / r=1 / r²=1 / COPY · · · · DRAW.
You should seea=2 b=3

12.5No data#

Example 12.15

CALC with empty lists

  1. Open Statistics and choose CALC, 1-VAR with nothing entered.

    MENU2F2F1
Result of the example "CALC with empty lists" The display shows: Dimension ERROR / Press:[EXIT].
You should seeDimension ERROR

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