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Classic Scientific 30 manual · Chapter 10 of 13

Data editor and statistics

Enter data in lists L1 to L3, then find one-variable statistics, two-variable statistics and regressions.

10.1Enter data in a list#

The data editor with three values in L1. The display shows: L1 | L2 | L3 / 4 | | / 6 | | / 8 | | / | | / L1(4)=.
The data editor with three values in L1.

Press data to open the data editor. It has three columns, L1, L2 and L3. The bottom line tells you which cell is selected. Type a number and press enter to store it and move down. Use ▶ and ◀ to change column and ▲ and ▼ to change row. delete removes the selected row of that list.

Example 10.1

Type three values

  1. Open the editor and type 4, 6 and 8.

    data4enter6enter8enter
Result of the example "Type three values" The display shows: L1 | L2 | L3 / 4 | | / 6 | | / 8 | | / | | / L1(4)=.
You should seeL1 4 6 8
Example 10.2

Remove a value

  1. Type 1, 2, 3, move up one row and press delete to remove the 3.

    data1enter2enter3enter▲delete
Result of the example "Remove a value" The display shows: L1 | L2 | L3 / 1 | | / 2 | | / | | / L1(3)=.
You should seeL1(3)=
Example 10.3

Clear a list

  1. In the editor, press data again and choose Clear L1.

    data1enter2enter3enterdata1
Result of the example "Clear a list" The display shows: L1 | L2 | L3 / | | / L1(4)=.
You should seeL1(4)=

See also Enter data into a list

10.2Find the mean and standard deviation of one list#

  1. 2ndstatdata
  2. 1-Var Stats
  3. enter (DATA)
  4. enter (FRQ)
Running 1-Var Stats.
xˉ=∑xn,Sx=∑(x−xˉ)2n−1,σx=∑(x−xˉ)2n\bar{x}=\frac{\sum x}{n},\qquad S_x=\sqrt{\frac{\sum (x-\bar{x})^2}{n-1}},\qquad \sigma_x=\sqrt{\frac{\sum (x-\bar{x})^2}{n}}
Mean, sample and population standard deviation.
The STAT menu. The display shows: STAT / 1:1-Var Stats / 2:2-Var Stats / 3:LinReg ax+b.
The STAT menu.

Press 2ndstatdata (STAT) and choose 1-Var Stats. A small form asks which list holds the data (DATA) and which list holds the frequencies (FRQ, or ONE if every value counts once). Press enter to move from field to field and to run it. Use ◀ and ▶ to change the choice in a field. The results appear as a list you scroll with ▼.

ResultMeaning
nHow many values.
x̄The mean.
SxSample standard deviation.
σxPopulation standard deviation.
Σx, Σx²Sum of the values and of their squares.
minX, Q1, Med, Q3, maxXThe five-number summary.
Example 10.4

Mean of 1 to 5

  1. Enter 1 to 5 in L1, then run 1-Var Stats with the start choices.

    data1enter2enter3enter4enter5enter2ndstatdata1enterenter
Result of the example "Mean of 1 to 5" The display shows: 1-Var:L1,1 / 1:n=5 / 2:x̄=3 / 3:Sx=1.58113883.
You should see1:n=5 2:x̄=3 3:Sx=1.58113883
Example 10.5

Scroll to the sums

  1. Scroll down to see the sums.

    data4enter6enter8enter2ndstatdata1enterenter▼▼▼
Result of the example "Scroll to the sums" The display shows: 3:Sx=2 / 4:σx=1.632993162 / 5:Σx=18 / 6:Σx²=116.
You should see5:Σx=18 6:Σx²=116
Example 10.6

Median and quartiles

  1. Scroll further down to see Q1, Med and Q3.

    data1enter2enter3enter4enter5enter2ndstatdata1enterenter▼▼▼▼▼▼▼▼▼▼
Result of the example "Median and quartiles" The display shows: 8:Q1=1.5 / 9:Med=3 / A:Q3=4.5 / B:maxX=5.
You should see8:Q1=1.5 9:Med=3 A:Q3=4.5
Example 10.7

Use frequencies

  1. Put the values in L1 and how many times each occurs in L2. Choose L2 as the FRQ.

    data1enter2enter3enter▶▲▲▲2enter1enter1enter2ndstatdata1enter▶▶enter
Result of the example "Use frequencies" The display shows: 1-Var:L1,L2 / 1:n=4 / 2:x̄=1.75 / 3:Sx=0.9574271078.
You should see1-Var:L1,L2 1:n=4 2:x̄=1.75

See also Find the mean and spread of one listUse frequencies (how many times each value occurs)Find the standard deviationFind the mean, median and mode

10.3Find statistics for two lists#

r=∑(x−xˉ)(y−yˉ)∑(x−xˉ)2 ∑(y−yˉ)2r=\frac{\sum (x-\bar x)(y-\bar y)}{\sqrt{\sum (x-\bar x)^2\,\sum (y-\bar y)^2}}
The correlation coefficient r.

Put the x values in L1 and the y values in L2. Choose 2-Var Stats from the STAT menu. You get n, the means, both standard deviations, the sums, and the line of best fit (a, b and the correlation r).

Example 10.8

Two-variable results

  1. Enter x = 1, 2, 3, 4 in L1 and y = 3, 5, 4, 7 in L2, then run 2-Var Stats.

    data1enter2enter3enter4enter▶▲▲▲▲3enter5enter4enter7enter2ndstatdata2enterenterenter
Result of the example "Two-variable results" The display shows: 2-Var / 1:n=4 / 2:x̄=2.5 / 3:Sx=1.290994449.
You should see2-Var 1:n=4 2:x̄=2.5
Example 10.9

Scroll to the line of best fit

  1. Scroll down to see a, b and r.

    data1enter2enter3enter4enter▶▲▲▲▲3enter5enter4enter7enter2ndstatdata2enterenterenter▼▼▼▼▼▼▼▼▼▼▼▼▼
Result of the example "Scroll to the line of best fit" The display shows: C:Σxy=53 / D:a=1.1 / E:b=2 / F:r=0.8315218406.
You should seeD:a=1.1 E:b=2 F:r=0.8315218406

See also Summarise paired data (x and y)Measure how strongly two lists are related

10.4Find a line, parabola or exponential of best fit#

y=ax+b,y=ax2+bx+c,y=a⋅bxy=ax+b,\qquad y=ax^2+bx+c,\qquad y=a\cdot b^{x}
The three curves that can be fitted.

STAT items 3, 4 and 5 fit a curve to the points in two lists: LinReg ax+b (a straight line), QuadraticReg (ax²+bx+c) and ExpReg (a·bˣ). Fill in the xDATA, yDATA and FRQ fields as in 2-Var Stats.

Example 10.10

Fit a straight line

  1. Enter x = 1, 2, 3, 4 and y = 3, 5, 4, 7, then choose LinReg ax+b.

    data1enter2enter3enter4enter▶▲▲▲▲3enter5enter4enter7enter2ndstatdata3enterenterenter
Result of the example "Fit a straight line" The display shows: y=ax+b / 1:a=1.1 / 2:b=2 / 3:r²=0.6914285714.
You should seey=ax+b 1:a=1.1 2:b=2 3:r²=0.6914285714
Example 10.11

Fit a parabola

  1. Choose QuadraticReg with the same data.

    data1enter2enter3enter4enter▶▲▲▲▲3enter5enter4enter7enter2ndstatdata4enterenterenter
Result of the example "Fit a parabola" The display shows: y=ax²+bx+c / 1:a=0.25 / 2:b=-0.15 / 3:c=3.25.
You should seey=ax²+bx+c 1:a=0.25 3:c=3.25
Example 10.12

Fit an exponential curve

  1. Choose ExpReg with the same data.

    data1enter2enter3enter4enter▶▲▲▲▲3enter5enter4enter7enter2ndstatdata5enterenterenter
Result of the example "Fit an exponential curve" The display shows: y=a*b^x / 1:a=2.535462764 / 2:b=1.260962102 / 3:r²=0.6992616773.
You should seey=a*b^x 1:a=2.535462764 2:b=1.260962102

See also Fit a straight line to dataFit a parabola to dataFit an exponential curve to data

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