Stats on the TI-84+

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

 Enter a new list STAT Choose 1:Edit (the default) Arrow over to the list (L1–L6) you want Type a number, hit ENTER; repeat 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 STAT Choose 1:Edit (the default) Arrow to list entry you want to change To delete the highlighted entry: DEL To change the highlighted entry: type a number, hit ENTER To insert an entry above the highlighted entry: INS   (= 2ND DEL) To quit the list editor: QUIT (= 2ND MODE)

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

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

 Find the mean or median This assumes that you have put a list in L1. STAT Choose 1:1-Var Stats (the default) ENTER ENTER Arrow down to x̄ 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. STAT Choose 1:1-Var Stats (the default) ENTER ENTER VARS Choose 5:Statistics Arrow down to maxX ENTER Press –   (the subtraction key) VARS Choose 5:Statistics Arrow down to minX ENTER 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. Find the population standard deviation: STAT Arrow over to CALC Choose 1:1-Var Stats (the default) ENTER ENTER Arrow down to find σx Find the population variance: VARS Choose 5:Statistics Arrow down to σx ENTER puts it on the main screen ENTER again to see its value x2 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. Find the sample standard deviation: STAT Arrow over to CALC Choose 1:1-Var Stats (the default) ENTER ENTER Arrow down to find Sx Find the sample variance: VARS Choose 5:Statistics Arrow down to Sx ENTER puts it on the main screen ENTER again to see its value x2 ENTER

 Find quartiles This assumes that you have put a list in L1. STAT Arrow over to CALC Choose 1:1-Var Stats (the default) ENTER ENTER 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. STAT Arrow over to CALC Choose 1:1-Var Stats (the default) ENTER 2ND 1 to get L1 Press , (the comma key) 2ND 2 to get L2 ENTER

 Use a computed statistic This assumes that you have put a list in L1. If you haven’t done so already, compute stats: STAT Arrow over to CALC Choose 1:1-Var Stats (the default) ENTER ENTER Use a computed stat: VARS Choose 5:Statistics Arrow down to the stat you want ENTER puts it on the main screen 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. STAT PLOT (= 2ND Y=) Arrow down to desired stat plot (default is 1) ENTER to get stat plot options Arrow to On and press ENTER Arrow to and press ENTER ENTER If Xlist is not already set to L1: Arrow down to Xlist (do not press ENTER) LIST (= 2ND STAT) ENTER Set Freq to 1 Use WINDOW to set window params: Set Xmin = lower limit of lowest class Set Xmax = upper limit of highest class Set Xscl = class width Set Ymin = 0 Set Ymax = a value near but ≥ max frequency (you may have to play with this) 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. STAT PLOT (= 2ND Y=) Arrow down to desired stat plot (default is 1) ENTER to get stat plot options Arrow to On and press ENTER Arrow to , press ENTER ENTER If Xlist is not already set to L1: Arrow down to Xlist (do not press ENTER) LIST (= 2ND STAT) ENTER Use WINDOW to set window params GRAPH

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

 Construct a scatter plot This assumes that you have put your x-coordinates in L1 and your y-coordinates in L2. STAT PLOT (= 2ND Y=) Arrow down to desired stat plot (default is 1) ENTER to get stat plot options Arrow to On and press ENTER Arrow to and press ENTER If Xlist is not already set to L1: Arrow down to Xlist (do not press ENTER) LIST (= 2ND STAT) ENTER If Ylist is not already set to L2: Arrow down to Xlist (do not press ENTER) LIST (= 2ND STAT) Arrow down to L2 ENTER Use WINDOW to set window params 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: DISTR (= 2ND VARS) Arrow down to binompdf ENTER Enter your values of n, p, and x, separated by commas 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: STAT Choose 1:Edit (the default) Arrow over to L1 Arrow up to the L1 list header LIST (= 2ND STAT) Arrow over to OPS Arrow down to 5: seq( ENTER to make seq( appear in list editor Press X,T,Θ,n , X,T,Θ,n , 0 , and then your value of n (you are entering X,X,0,n) ENTER Now get the binomial probabilities into L2: Arrow over to L2 Arrow up to the L2 list header DISTR (= 2ND VARS) Arrow down to binompdf( Enter n and p, separated by a comma 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 Put the probabilities from your binomial distribution into List L2 LIST (= 2ND STAT) Arrow over to MATH Arrow down to 5:sum( ENTER Enter the key sequence 2ND 2 , Enter your value of x, then a comma, then your value of n ENTER

 Probabilities for x~N(μ,σ) Given c, find P(x

 Construct a normal probability plot This assumes that you have put the data in L1. STAT PLOT (= 2ND Y=) Arrow down to desired stat plot (default is 1) ENTER to get stat plot options Arrow to On and press ENTER Arrow down, then over to , press ENTER If Data List is not already set to L1: Arrow down to Data List (do not press ENTER) LIST (= 2ND STAT) ENTER Arrow down to Data Axis Arrow to X ENTER ZOOM Choose 9:ZoomStat ENTER 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 x̄; and       . STAT Arrow to TESTS Choose 7:ZInterval Arrow to Stats and press ENTER Arrow down to σ and enter the value of σ Arrow down to x̄ and enter the value Arrow down to n:. Set it to your value of n. Arrow down to C-Level: (confidence level) and set it (as a decimal) Arrow down to Calculate 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: STAT Arrow to TESTS Choose 8:TInterval Arrow to Data and press ENTER If List: is not already set to L1: Arrow down to List: (do not press ENTER) LIST (= 2ND STAT) ENTER Arrow down to Freq:. Set it to 1. Arrow down to C-Level: (confidence level) and set it (as a decimal) Arrow down to Calculate ENTER   If you know       the sample size n;       the sample mean x̄; and        STAT Arrow to TESTS Choose 8:TInterval Arrow to Stats and press ENTER Arrow down to x̄ and enter the value Arrow down to Sx and enter the value Arrow down to n:. Set it to your value of n. Arrow down to C-Level: (confidence level) and set it (as a decimal) Arrow down to Calculate 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 sample mean x̄; and       the sample size n. STAT Arrow to TESTS Choose 1:Z-Test Arrow to Stats and press ENTER Arrow down to μ0: and enter the value Arrow down to σ: and enter the value Arrow down to x̄: and enter the value Arrow down to n: and enter the value Arrow down to the line beginning μ:≠μ0 and choose your alternate hypothesis ENTER Arrow down to Calculate 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: STAT Arrow to TESTS Choose 2:T-Test Arrow to Data and press ENTER Arrow down to μ0: and enter the value If List: is not already set to L1: Arrow down to List: (do not press ENTER) LIST (= 2ND STAT) ENTER Arrow down to Freq:. Set it to 1. Arrow down to the line beginning μ:≠μ0 and choose your alternate hypothesis ENTER Arrow down to Calculate ENTER   If you know       the sample size n;       the sample mean x̄;        STAT Arrow to TESTS Choose 2:T-Test Arrow to Stats and press ENTER Arrow down to μ0: and enter the value Arrow down to x̄ and enter the value Arrow down to Sx and enter the value Arrow down to n: and enter the value Arrow down to the line beginning μ:≠μ0 and choose the alternate hypothesis ENTER Arrow down to Calculate ENTER

 r and trendline coefficients This assumes that you have put your x-coordinates in L1 and your y-coordinates in L2. STAT Arrow over to CALC Choose 4:LinReg(ax+b) ENTER 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. Get the coefficients a and b. Write them down. Put ax+b in Y1: Press Y= Arrow to \Y1= Type in the number you got for a Press the * (multiply) key Press the X,T,Θ,n key (to get X) Press + Type in the number you got for b 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: STAT Arrow over to EDIT if necessary Arrow to 1:Edit ENTER Arrow over to L3 Arrow up to the list header for L3 Enter the key sequence ( 2ND 1 - 2ND 2 ) x2 ÷ 2ND 2 ENTER QUIT (= 2ND MODE) LIST (= 2ND STAT) Arrow over to MATH Arrow down to 5:sum( ENTER 2ND 3 ) ENTER Compute the p-value: DISTR (= 2ND VARS) Arrow down to χ2cdf ENTER Enter the value of χ2 you found above, then a comma, then 100, then a comma, then the number of degrees of freedom ENTER

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

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