Stats on the TI-84+

Topics
Lists and Matrices
  Enter a new list
  Edit an existing list
  Clear a list
  Enter or edit a matrix
Descriptive statistics
  Find the mean or median
  Find the range
  Find the population variance or standard deviation
  Find the sample variance or standard deviation
  Find quartiles
  Stats for grouped data
  Use a computed statistic
Displays
  Construct a frequency histogram
  Construct a box-and-whisker plot
  Construct a line graph
  Construct a scatter plot
The binomial distribution
  Binomial distribution: probability of exactly x successes
  Binomial distribution
  Binomial distribution: probability of at least x successes
The normal distribution
  Probabilities for x~N(μ,σ)
  Construct a normal probability plot
Confidence intervals
  z Confidence interval (σ known)
  t Confidence interval (σ unknown)
Hypothesis tests
  Z-Test (σ known)
  T-Test (σ unknown)
Correlation and regresssion
  r and trendline coefficients
  Add a trendline to a scatter plot
Chi-square
  Chi-square goodness-of-fit test
  Chi-square goodness-of-fit test for the TI-84+ only
  Chi-square independence test


Notation
On the TI-84+:
    Sx means the sample standard deviation s
    σx means the population standard deviation σ

Problems and Errors
INVALID DIM when graphing
  1. You may have several functions defined, one of which is invalid under the current conditions. Press Y= and clear them.
  2. You may have multiple plots turned on. Press Y= and make sure that only one of Plot 1, Plot 2, or Plot 3 is highlighted.
  3. If you are using multiple lists, you may have two lists of different lengths.
  4. You may have deleted a built-in list. Press STAT, then 5, then ENTER.
List L1 is gone
  1. STAT
  2. Choose 5:SetUpEditor
  3. ENTER
Normal probability plot does not appear
   Press ZOOM, then 9.
 
LinReg does not show r
  1. CATALOG (= 2ND 0)
  2. x-1 (to get to the Ds)
  3. Arrow down to DiagnosticOn
  4. ENTER
Weird error which won't go away
   Try resetting all RAM, which erases temporary memory only:
  1. MEM (= 2ND +)
  2. Choose 7:Reset
  3. Choose 1:All RAM
  4. Choose 2:Reset
  5. ENTER
   Try resetting defaults:
  1. MEM (= 2ND +)
  2. Choose 7:Reset
  3. Choose 2:Defaults
  4. Choose 2:Reset
  5. ENTER
   If these don't work, you need an expert (not me, I'm afraid).

Enter a new list
  1. STAT
  2. Choose 1:Edit (the default)
  3. Arrow over to the list (L1–L6) you want
  4. Type a number, hit ENTER; repeat
  5. Quit the list editor: QUIT (= 2ND MODE)
If you chose list L1, your list will be stored in the variable L1 (= 2ND 1), and so on.

Edit an existing list
  1. STAT
  2. Choose 1:Edit (the default)
  3. Arrow to list entry you want to change
  4. To delete the highlighted entry: DEL
  5. To change the highlighted entry: type a number, hit ENTER
  6. To insert an entry above the highlighted entry: INS   (= 2ND DEL)
  7. To quit the list editor: QUIT (= 2ND MODE)

Clear a list
  1. STAT
  2. Choose 1:Edit (the default)
  3. Arrow over to the list you want to clear
  4. Arrow up to highlight the list name
  5. CLEAR
  6. ENTER
  7. To quit the list editor: QUIT (= 2ND MODE)

Enter or edit a matrix
  1. MATRIX (= 2ND x-1)
  2. Arrow over to EDIT
  3. Arrow down to the matrix you wish to edit
  4. ENTER
  5. Enter the number of rows and press ENTER
  6. Enter the number of columns and press ENTER
  7. Enter the matrix entries, pressing ENTER after each
  8. To quit the matrix editor: QUIT (= 2ND MODE)

Find the mean or median
This assumes that you have put a list in L1.
  1. STAT
  2. Choose 1:1-Var Stats (the default)
  3. ENTER
  4. ENTER
  5. Arrow down to or Med
    To use the mean or median in a computation, see the section on using a computed statistic.

Find the range
This assumes that you have put a list in L1.
 
    Your calculator does not find the range explicitly. Instead you must compute xmax xmin.
  1. STAT
  2. Choose 1:1-Var Stats (the default)
  3. ENTER
  4. ENTER
  5. VARS
  6. Choose 5:Statistics
  7. Arrow down to maxX
  8. ENTER
  9. Press   (the subtraction key)
  10. VARS
  11. Choose 5:Statistics
  12. Arrow down to minX
  13. ENTER
  14. ENTER

Find population variance or standard deviation
This assumes that you have put a list in L1.
    Your calculator does not find the population variance directly. You find the population standard deviation and square it.
  1. Find the population standard deviation:
    1. STAT
    2. Arrow over to CALC
    3. Choose 1:1-Var Stats (the default)
    4. ENTER
    5. ENTER
    6. Arrow down to find σx

  2. Find the population variance:
    1. VARS
    2. Choose 5:Statistics
    3. Arrow down to σx
    4. ENTER puts it on the main screen
    5. ENTER again to see its value
    6. x2
    7. ENTER

Find sample variance or standard deviation
This assumes that you have put a list in L1.
    Your calculator does not find the sample variance directly. You find the sample standard deviation and square it.
  1. Find the sample standard deviation:
    1. STAT
    2. Arrow over to CALC
    3. Choose 1:1-Var Stats (the default)
    4. ENTER
    5. ENTER
    6. Arrow down to find Sx

  2. Find the sample variance:
    1. VARS
    2. Choose 5:Statistics
    3. Arrow down to Sx
    4. ENTER puts it on the main screen
    5. ENTER again to see its value
    6. x2
    7. ENTER

Find quartiles
This assumes that you have put a list in L1.
  1. STAT
  2. Arrow over to CALC
  3. Choose 1:1-Var Stats (the default)
  4. ENTER
  5. ENTER
  6. Arrow down to find Q1, Med, and Q3

Stats for grouped data
This assumes that you have put your data (or midpoints) in L1 and your frequencies in L2.
  1. STAT
  2. Arrow over to CALC
  3. Choose 1:1-Var Stats (the default)
  4. ENTER
  5. 2ND 1 to get L1
  6. Press , (the comma key)
  7. 2ND 2 to get L2
  8. ENTER

Use a computed statistic
This assumes that you have put a list in L1.
  1. If you haven’t done so already, compute stats:
    1. STAT
    2. Arrow over to CALC
    3. Choose 1:1-Var Stats (the default)
    4. ENTER
    5. ENTER
  2. Use a computed stat:
    1. VARS
    2. Choose 5:Statistics
    3. Arrow down to the stat you want
    4. ENTER puts it on the main screen
    5. If you wish, ENTER again to see its value
You can select a variable from VARS at any time. To see an example of this within a calculation, see the section on range.

Construct a frequency histogram
This assumes that you have put the data in L1.
  1. STAT PLOT (= 2ND Y=)
  2. Arrow down to desired stat plot (default is 1)
  3. ENTER to get stat plot options
  4. Arrow to On and press ENTER
  5. Arrow to and press ENTER
  6. ENTER
  7. If Xlist is not already set to L1:
    1. Arrow down to Xlist (do not press ENTER)
    2. LIST (= 2ND STAT)
    3. ENTER
  8. Set Freq to 1
  9. Use WINDOW to set window params:
    1. Set Xmin = lower limit of lowest class
    2. Set Xmax = upper limit of highest class
    3. Set Xscl = class width
    4. Set Ymin = 0
    5. Set Ymax = a value near but ≥ max frequency (you may have to play with this)
  10. GRAPH

Construct a box-and-whisker plot
This assumes that you have put a list in L1 consisting of xmin, Q1, Q2, Q3, and xmax in that order.
  1. STAT PLOT (= 2ND Y=)
  2. Arrow down to desired stat plot (default is 1)
  3. ENTER to get stat plot options
  4. Arrow to On and press ENTER
  5. Arrow to , press ENTER
  6. ENTER
  7. If Xlist is not already set to L1:
    1. Arrow down to Xlist (do not press ENTER)
    2. LIST (= 2ND STAT)
    3. ENTER
  8. Use WINDOW to set window params
  9. GRAPH

Construct a line graph
This assumes that you have put your x-coordinates in L1 and your y-coordinates in L2.
  1. STAT PLOT (= 2ND Y=)
  2. Arrow down to desired stat plot (default is 1)
  3. ENTER to get stat plot options
  4. Arrow to On and press ENTER
  5. Arrow to and press ENTER
  6. If Xlist is not already set to L1:
    1. Arrow down to Xlist (do not press ENTER)
    2. LIST (= 2ND STAT)
    3. ENTER
  7. If Ylist is not already set to L2:
    1. Arrow down to Xlist (do not press ENTER)
    2. LIST (= 2ND STAT)
    3. Arrow down to L2
    4. ENTER
  8. Use WINDOW to set window params
  9. GRAPH

Construct a scatter plot
This assumes that you have put your x-coordinates in L1 and your y-coordinates in L2.
  1. STAT PLOT (= 2ND Y=)
  2. Arrow down to desired stat plot (default is 1)
  3. ENTER to get stat plot options
  4. Arrow to On and press ENTER
  5. Arrow to and press ENTER
  6. If Xlist is not already set to L1:
    1. Arrow down to Xlist (do not press ENTER)
    2. LIST (= 2ND STAT)
    3. ENTER
  7. If Ylist is not already set to L2:
    1. Arrow down to Xlist (do not press ENTER)
    2. LIST (= 2ND STAT)
    3. Arrow down to L2
    4. ENTER
  8. Use WINDOW to set window params
  9. GRAPH
You can add a trendline to a scatter plot.

Binomial distribution: probability of exactly x successes
To find the probability of exactly x successes in n Bernoulli trials with P(success) = p:
  1. DISTR (= 2ND VARS)
  2. Arrow down to binompdf
  3. ENTER
  4. Enter your values of n, p, and x, separated by commas
  5. ENTER

Binomial distribution
To display a binomial distribution for n trials each having P(success) = p
Lists L1 and L2 should be cleared before beginning.
 
First get the numbers of successes into L1:
  1. STAT
  2. Choose 1:Edit (the default)
  3. Arrow over to L1
  4. Arrow up to the L1 list header
  5. LIST (= 2ND STAT)
  6. Arrow over to OPS
  7. Arrow down to 5: seq(
  8. ENTER to make seq( appear in list editor
  9. Press X,T,Θ,n , X,T,Θ,n , 0 , and then your value of n (you are entering X,X,0,n)
  10. ENTER
Now get the binomial probabilities into L2:
  1. Arrow over to L2
  2. Arrow up to the L2 list header
  3. DISTR (= 2ND VARS)
  4. Arrow down to binompdf(
  5. Enter n and p, separated by a comma
  6. ENTER

Binomial distribution: probability of at least x successes
To find the probability of at least x successes in n Bernoulli trials with P(success) = p
  1. Put the probabilities from your binomial distribution into List L2
  2. LIST (= 2ND STAT)
  3. Arrow over to MATH
  4. Arrow down to 5:sum(
  5. ENTER
  6. Enter the key sequence 2ND 2 ,
  7. Enter your value of x, then a comma, then your value of n
  8. ENTER

Probabilities for x~N(μ,σ)

Given c, find P(x<c):

  Use normalcdf(-10000,c,μ,σ):
  1. DISTR (= 2ND VARS)
  2. Arrow down to normalcdf(
  3. ENTER to put normalcdf( on the screen
  4. Type in the values, separated by commas
  5. ENTER

Given a probability p, find c such that P(x<c) = p:

  Use invNorm(p,μ,σ):
  1. DISTR (= 2ND VARS)
  2. Arrow down to invNorm(
  3. ENTER to put invNorm( on the screen
  4. Type in the values, separated by commas
  5. ENTER

Construct a normal probability plot
This assumes that you have put the data in L1.
  1. STAT PLOT (= 2ND Y=)
  2. Arrow down to desired stat plot (default is 1)
  3. ENTER to get stat plot options
  4. Arrow to On and press ENTER
  5. Arrow down, then over to , press ENTER
  6. If Data List is not already set to L1:
    1. Arrow down to Data List (do not press ENTER)
    2. LIST (= 2ND STAT)
    3. ENTER
  7. Arrow down to Data Axis
  8. Arrow to X
  9. ENTER
  10. ZOOM
  11. Choose 9:ZoomStat
  12. ENTER
  13. GRAPH (if necessary)

z Confidence interval (σ known)
You must either know that the population is approximately normal, or have n ≥ 30 (or both).

  You will need
      the sample size n;
      the sample mean ; and
      the population standard deviation σx.
  1. STAT
  2. Arrow to TESTS
  3. Choose 7:ZInterval
  4. Arrow to Stats and press ENTER
  5. Arrow down to σ and enter the value of σ
  6. Arrow down to and enter the value
  7. Arrow down to n:. Set it to your value of n.
  8. Arrow down to C-Level: (confidence level) and set it (as a decimal)
  9. Arrow down to Calculate
  10. ENTER

t Confidence interval (σ unknown)
You must be able to apply the CLT.

There are different procedures depending on whether you have data or stats.


  If you have put the data in L1:
  1. STAT
  2. Arrow to TESTS
  3. Choose 8:TInterval
  4. Arrow to Data and press ENTER
  5. If List: is not already set to L1:
    1. Arrow down to List: (do not press ENTER)
    2. LIST (= 2ND STAT)
    3. ENTER
  6. Arrow down to Freq:. Set it to 1.
  7. Arrow down to C-Level: (confidence level) and set it (as a decimal)
  8. Arrow down to Calculate
  9. ENTER
  If you know
      the sample size n;
      the sample mean ; and
      the sample standard deviation Sx:
  1. STAT
  2. Arrow to TESTS
  3. Choose 8:TInterval
  4. Arrow to Stats and press ENTER
  5. Arrow down to and enter the value
  6. Arrow down to Sx and enter the value
  7. Arrow down to n:. Set it to your value of n.
  8. Arrow down to C-Level: (confidence level) and set it (as a decimal)
  9. Arrow down to Calculate
  10. ENTER

Z-Test (σ known)
You must know either that the population is approximately normal, or have n ≥ 30 (or both).

  You will need
      μ0;
      the population standard deviation σx;
      the sample mean ; and
      the sample size n.
  1. STAT
  2. Arrow to TESTS
  3. Choose 1:Z-Test
  4. Arrow to Stats and press ENTER
  5. Arrow down to μ0: and enter the value
  6. Arrow down to σ: and enter the value
  7. Arrow down to x̄: and enter the value
  8. Arrow down to n: and enter the value
  9. Arrow down to the line beginning μ:≠μ0 and choose your alternate hypothesis
  10. ENTER
  11. Arrow down to Calculate
  12. ENTER

T-Test (σ unknown)
You must be able to apply the CLT.

There are different procedures depending on whether you have data or stats.


  If you have put the data in L1:
  1. STAT
  2. Arrow to TESTS
  3. Choose 2:T-Test
  4. Arrow to Data and press ENTER
  5. Arrow down to μ0: and enter the value
  6. If List: is not already set to L1:
    1. Arrow down to List: (do not press ENTER)
    2. LIST (= 2ND STAT)
    3. ENTER
  7. Arrow down to Freq:. Set it to 1.
  8. Arrow down to the line beginning μ:≠μ0 and choose your alternate hypothesis
  9. ENTER
  10. Arrow down to Calculate
  11. ENTER
  If you know
      the sample size n;
      the sample mean ;
      the sample standard deviation Sx:
  1. STAT
  2. Arrow to TESTS
  3. Choose 2:T-Test
  4. Arrow to Stats and press ENTER
  5. Arrow down to μ0: and enter the value
  6. Arrow down to and enter the value
  7. Arrow down to Sx and enter the value
  8. Arrow down to n: and enter the value
  9. Arrow down to the line beginning μ:≠μ0 and choose the alternate hypothesis
  10. ENTER
  11. Arrow down to Calculate
  12. ENTER

r and trendline coefficients
This assumes that you have put your x-coordinates in L1 and your y-coordinates in L2.
  1. STAT
  2. Arrow over to CALC
  3. Choose 4:LinReg(ax+b)
  4. ENTER
  5. ENTER
Numbers a, b, r, and r2 should be displayed. If r or r2 is not displayed, see the Problems and errors section.

Add a trendline to a scatter plot
This assumes that you have put your x-coordinates in L1 and your y-coordinates in L2 and made a scatter plot.
  1. Get the coefficients a and b. Write them down.
  2. Put ax+b in Y1:
    1. Press Y=
    2. Arrow to \Y1=
    3. Type in the number you got for a
    4. Press the * (multiply) key
    5. Press the X,T,Θ,n key (to get X)
    6. Press +
    7. Type in the number you got for b
  3. GRAPH

Chi-square goodness-of-fit test
If you have a TI-84+, you may be able to perform this test more simply.
This assumes that you have put your observed values in L1 and your expected values in L2 and that you have cleared List L3. There are two stages to the procedure.
Compute χ2:
  1. STAT
  2. Arrow over to EDIT if necessary
  3. Arrow to 1:Edit
  4. ENTER
  5. Arrow over to L3
  6. Arrow up to the list header for L3
  7. Enter the key sequence ( 2ND 1 - 2ND 2 ) x2 ÷ 2ND 2 ENTER
  8. QUIT (= 2ND MODE)
  9. LIST (= 2ND STAT)
  10. Arrow over to MATH
  11. Arrow down to 5:sum(
  12. ENTER
  13. 2ND 3 ) ENTER
Compute the p-value:
  1. DISTR (= 2ND VARS)
  2. Arrow down to χ2cdf
  3. ENTER
  4. Enter the value of χ2 you found above, then a comma, then 100, then a comma, then the number of degrees of freedom
  5. ENTER

Chi-square independence test
This assumes that you have put your observed values in Matrix A and your expected values in Matrix B.
  1. STAT
  2. Arrow over to TESTS
  3. Arrow down to χ2-Test
  4. ENTER
  5. If Matrix A is not already assigned to Observed:
    1. Arrow down to Observed:
    2. MATRIX (= 2ND x-1)
    3. Arrow to [A] if necessary
    4. ENTER
  6. If Matrix B is not already assigned to Expected:
    1. Arrow down to Expected:
    2. MATRIX (= 2ND x-1)
    3. Arrow to [B]
    4. ENTER
  7. Arrow down to Calculate
  8. ENTER

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