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Classic Graphing 84 manual · Chapter 13 of 25

One- and two-variable statistics

Summarise a list with 1-Var Stats (mean, standard deviation, quartiles), study pairs with 2-Var Stats, and use frequency lists.

13.1Find the mean, standard deviation and quartiles#

Press stat, then ▶ for CALC, then 1 for 1-Var Stats. A small form asks for the list (L1 unless you change it) and an optional frequency list. Move down to Calculate and press enter. The results appear on a scrolling screen; use ▼ to see the rest.

  1. stat
  2. ▶ CALC
  3. 1-Var Stats
  4. List: L1
  5. Calculate enter
Summarise a list
The 1-Var Stats form. The display shows: 1-Var Stats / List:L1 / FreqList: / Calculate.
The 1-Var Stats form.
sx=∑x2−nxˉ2n−1,σx=∑x2−nxˉ2ns_x=\sqrt{\frac{\sum x^2-n\bar{x}^2}{n-1}},\qquad \sigma_x=\sqrt{\frac{\sum x^2-n\bar{x}^2}{n}}
Sx is the sample standard deviation; σx is the population standard deviation.
Example 13.1

Statistics of 1, 2, 3, 4, 5

  1. Enter the data in L1.

    stat11enter2enter3enter4enter5enter

  2. Open 1-Var Stats, move down to Calculate and press enter.

    stat▶1▼▼enter
Result of the example "Statistics of 1, 2, 3, 4, 5" The display shows: 1-Var Stats / x̄=3 / Σx=15 / Σx²=55 / Sx=1.58113883 / σx=1.414213562 / n=5 / minX=1 ↓.
You should seex̄=3 Σx=15 Σx²=55 Sx=1.58113883 σx=1.414213562 n=5
Example 13.2

Scroll to the quartiles

  1. Press down four more times.

    stat11enter2enter3enter4enter5enterstat▶1▼▼enter▼▼▼▼
Result of the example "Scroll to the quartiles" The display shows: 1-Var Stats / σx=1.414213562 ↑ / 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

The results are stored as statistics variables. Paste them from vars then 5 (Statistics…): for example x̄ is in the XY tab. They stay until the next calculation.

Example 13.3

Use the mean on the home screen

  1. Run 1-Var Stats on 1 to 5 and leave with clear.

    stat11enter2enter3enter4enter5enterstat▶1▼▼enterclear

  2. Press vars, 5, 2 (x̄) and enter.

    vars52enter
Result of the example "Use the mean on the home screen" The display shows: minX=1 / Q1=1.5 / Med=3 / Q3=4.5 / maxX=5 / x̄ / 3.
You should see3

13.2Use a frequency list#

If each value occurs several times, put the values in L1 and how often each occurs in L2, then enter L2 as the FreqList.

Example 13.4

Mean with frequencies

xˉ=1⋅3+2⋅13+1=1.25\bar{x}=\frac{1\cdot3+2\cdot1}{3+1}=1.25

  1. L1 = 1, 2 and L2 = 3, 1.

    stat11enter2enter▶3enter1enter

  2. Open 1-Var Stats, move down to FreqList, type L2, then down to Calculate and enter.

    stat▶1▼2ndL22▼enter
Result of the example "Mean with frequencies" The display shows: 1-Var Stats / x̄=1.25 / Σx=5 / Σx²=7 / Sx=.5 / σx=.4330127019 / n=4 / minX=1 ↓.
You should seex̄=1.25 n=4

13.3Statistics for pairs of data (2-Var Stats)#

2-Var Stats uses an Xlist and a Ylist and gives the means, deviations, sums and extremes of both, plus Σxy.

Example 13.5

Two lists

  1. L1 = 1, 2, 3 and L2 = 2, 4, 6.

    stat11enter2enter3enter▶2enter4enter6enter

  2. Open 2-Var Stats, go down to Calculate and press enter, then scroll down 6 lines.

    stat▶2▼▼▼enter▼▼▼▼▼▼
Result of the example "Two lists" The display shows: 2-Var Stats / ȳ=4 ↑ / Σy=12 / Σy²=56 / Sy=2 / σy=1.632993162 / Σxy=28 / minX=1 ↓.
You should seeΣxy=28

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