Download a "guidebook" (manual) at the TI site
Access a Named Distribution
The calculator has built-in functions for some of the named distributions.
You can access them from the Catalog or through the DIST button.
2ND-DISTR, then cursor down to the desired entry.
For example, cursor to A, below 0, for binompdf(
Alternatively, 2nd-CATALOG, then type the first letter of the distribution since you'll be in
alpha mode, and cursor to the desired one. Example, type B, then scroll to binompdf( .
ENTER will paste this in. Then you can enter the required and optional parameters.
Distributions below: Normal, Student-t, Chi-Squared, F, Binomial, Poisson, Geometric
| 1: normalpdf(x [, μ, σ])
5: tpdf(x, df) 7: χ2pdf(x, df) 9: Fpdf(x, dfNum, dfDen) |
y-value of the named continuous probability density function at the stated x-value. Use of the variable X is useful for graphing. Example: define Y1 = normalpdf(X), set the Window, and Graph. |
| 2: normalcdf(x1, x2 [, μ, σ])
6: tcdf(x1, x2,df) 8: χ2cdf(x1, x2,df) 0: Fcdf(x1, x2, dfNum, dfDen) |
Based on the named continuous cumulative distribution; yields the area under the named curve between x1 and x2. |
| 3: invNorm(area [, μ, σ])
4: invT(area, df) |
Calculates the x value associated with an area to the left of the x-value under the named pdf. |
| A: binompdf(n, p [, x])
C: poissonpdf(λ, x) E: geometpdf(p, x) |
y=value of the named discrete probability mass function. We can calculate a single value, create a table of values, or calculate lists of values. Each function is usually graphed as a histogram as described below. x can also be a list of values rather than a single value. |
| B: binomcdf(n, p [, x])
D: poissoncdf(λ, x) F: geometcdf(p, x) |
The named discrete cumulative distribution function; area under the named curve at and to the left of x. x can also be a list of values rather than a single value. |
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Calculate and plot discrete probabilities
Example: binomial distribution with n=5, p=.2.
STAT/EDIT. Clear lists L1 and L2. In L1, enter {0, 1, 2, 3, 4, 5}.
ursor up to the name L2. L2=binom(5, .2, L1) ENTER.
continue to make a histogram from these lists.
If a distribution is not one that is built into the calculator, (like dice)
treat it as data and enter it into the lists as described elsewhere.
Calculate some discrete probability values
Examples, Method 1: geometpdf(.2, {0,1,2,3,4}) .
binompdf(5, .2) .
binompdf(10, .3, {0, 2, 8}) .
Examples, Method 2: Y1 = binompdf(5, .2, X)
2nd-TBLSET ENTER.
TbleStart = 0. ENTER.
ΔTbl = 1 ENTER.
Indpnt: Auto ENTER.
Depend: Auto ENTER.
2nd-TABLE
Plot a named continuous distribution, Example: normal distribution with &mu=70, &sigma=8. Y1 = normalpdf(X,70,8). graph. Adjust the window settings.
Statistical analysis on one variable
Enter the data into L1 (or another list).
STAT/CALC/1-Var Stats to paste this command into the home screen.
For each STAT CALC menu item, if neither Xlistname nor Ylistname is specified,
then the default list names are L1 and L2. If you do not specify freqlist, then the default is 1
occurrence of each list element.
Note: Sx is the sample standard deviation; used for data.
sx is the population standard deviation; used for probability.
Remember that we use population statistics when we are certain that we have absolutely all of the data.
It is rare that we will need
Sx, which is the sum of the data,
or Sx2, which is the sum of the squares of the data.
For IQR, you will calculate Q3-Q1 (the calculator doesn't show it.)
Restore a list that no longer shows up on the Stat menu... Stat/Edit move the cursor onto the name, such as L3, where you wish to insert a list. 2nd-INS for insert; now you should see "Name=" at the bottom of the screen. from here, 2nd-L1 works, or you can select a list name through 2nd-LIST/NAMES/ and scroll to the name.
Enter Data into a list STAT/EDIT In general, use L1 for x-values. If there are y-values, use L2. I suggest you clear specified lists for each new problem: from the STAT LIST editor, cursor up onto a list name, and then press CLEAR (not DEL) and ENTER. Then type the data.
Access values of calculated statistics (like the mean), so that the exact value can be used, Enter data and calculate the appropriate statistics. (If you edit a list or change the type of analysis, all stat variables are cleared and will need to be re-calculated.) VARS/5:Statistics, and select the appropriate menu. For instance, here are some common statistics and the menu in which each is found.
| XY | Σ | PTS |
| number of data points
mean standard deviation min max |
sum of x's
sum of squared x's |
1st quartile
median 3rd quartile |
Statistical plot types Instructions for setting up other one-variable plots are similar to those for the histogram. In order of appearance on the calculator:
| scatter | xyLine (not used in Stat or Prob |
histogram |
| "modified" box plot that shows outliers; the one we will use. | boxplot that doesn't show outliers. do not use. | normal probability plot. Typically select Y for the DataAxis setting. |
Create a histogram
Enter the data into L1 (or another list). If you have just a list of values (like {70, 80, 70, 90}),
you're finished entering data; in this case, enter "1" for "Freq" below.
If, however, the data comes with counts (absolute frequencies) or probabilities (relative frequencies),
then enter these into L2 (or another list); in this case, enter this list for "Freq" below.
Deselect all graphs and statistical plots. Make sure the graph mode is set to function.
Define the plot.
2ND-[STAT PLOT] (above y=).
cursor up to Plot1 (or whichever) ENTER.
cursor to "On" ENTER
cursor to "Type =" cursor to the rightmost on the top row.
ENTER.
cursor to "Data List:" 2ND-LIST
select list ENTER
cursor to "Data List:" 2ND-LIST
select list ENTER
Set Freq to 1 or L2, as appropriate.
ZOOM/ZOOMSTAT after graphing for a reasonable amount of data.
If the histogram is unsatisfactory,
change the window settings manually. Make sure that xmin and ymin are a bit smaller than the values,
and xmax and ymax are a bit bigger, so that the histogram plots well. xscl controls the bin width,
which in turn affects the number of bins.
TRACE to see the important values for each bin, especially to record your graph by hand on paper.
Record the x-value cut offs for each bin. "n" is the frequency or relative frequency; indicate these on the y-axis.
Normal Distribution Areas
De-select all plots, including StatPlots.
Define the window settings for graphing. Remember that 4 standard deviations on either side of the mean
shows practically all of a normal distribution; the y-values are between 0 and 1.
2nd-[DRAW] DRAW 1:ClrDraw ENTER.
this clears any previous drawings.
You MUST do this between each drawing (or you'll get wacky results.)
Because these are "drawings" and not "graphs", the Graph button is useless; there's nothing in
the y= menu or defined in a StatPlot to graph.
2nd-[DIST] DRAW 1:ShadeNorm(
give the values for the lower value and upper value, then close with ) if this is for a standard normal.
If, however, it is not a standard normal, then include the mean first, then the standard deviation;
then close with ). Separate these values with commas.
Example: We want Prob{-0.5 < Z < 0.5} for a standard normal. Good window settings are
Xmin=-4, Xmax=4, Xscl=1, Ymin=-0.2, Ymax=0.8, Yscl=0.2,Xres=1.
2ND-DISTR/(cursor down to A, below 0):binompdf( ENTER.
(or select binompdf( from the Catalog).
5, .2, L1) ENTER. (This uses the values in L1 as the x-values.)
Set up a histogram but manually set xscl to 1.
Alternatively, use the table features. Y1= binompdf( 5,.2, (hit the button "X,T,θ,n" to get the X) 2nd-TBLSET. TblStart=0. ΔTbl=1. Indpnt: Auto.
Distribution Areas
Example: a Normal distribution.
De-select all plots, including StatPlots.
Define the window settings for graphing. Remember that 4 standard deviations on either side of the mean
shows practically all of a normal distribution; the y-values are between 0 and 1.
2nd-[DRAW] DRAW 1:ClrDraw ENTER.
this clears any previous drawings.
You MUST do this between each drawing (or you'll get wacky results.)
Because these are "drawings" and not "graphs", the Graph button is useless; there's nothing in
the y= menu or defined in a StatPlot to graph.
2nd-[DIST] DRAW 1:ShadeNorm(
give the values for the lower value and upper value, then close with ) if this is for a standard normal.
If, however, it is not a standard normal, then include the mean first, then the standard deviation;
then close with ). Separate these values with commas.
Example We want Prob{-0.5 < Z < 0.5} for a standard normal. Good window settings are
Xmin=-4, Xmax=4, Xscl=1, Ymin=-0.2, Ymax=0.8, Yscl=0.2,Xres=1.
2nd-[DIST] DRAW 1:ShadeNorm( -.5,.5)
Example We want Prob{55 < X < 62} for a normal distribution with mean 60 and standard deviation 7.
4 std devs from the mean yields 60 - 4*7 = 32, 60 + 4*7 = 88.
Good window settings are
Xmin=30, Xmax=90, Xscl=10,
Ymin=-0.1, Ymax=0.1, Yscl=0.2,Xres=1.
2nd-[DIST] DRAW 1:ShadeNorm(55,62,60,7)
TIP: If you have to fiddle with the window settings, 2nd-QUIT from the drawing, change the
window settings, then 2nd-ENTRY ENTER.
Creating a scatterplot without regression line Enter the data into two lists. Deselect all graphs and statistical plots. Make sure the graph mode is set to function.
Either do the following prior to graphing or use ZOOM/ZOOMSTAT after graphing.
ZOOM/ZOOMSTAT adjusts the window settings to include all values.
Perform a "two variable statistics" to obtain the settings for the graphing window.
Use the WINDOW button to change these settings.
Use the min and the max of the x-data to set xmin and xmax on the graphing window.
Use the min and the max of the y-data to set ymin and ymax on the graphing window.
Xlist and Ylist must be the same length.
Define the plot.
2ND-[STAT PLOT] (above y=).
cursor up to Plot1 (or whichever) ENTER.
cursor to "Type =" (use the first one)
cursor to "Xlist:" 2ND-LIST
select list ENTER
cursor to "Ylist:" 2ND-LIST
select list ENTER
GRAPH
optional resizing: ZOOM 9:ZOOM/ZOOMSTAT; ENTER
(or manually change the window settings.)
Displaying the correlation coefficient
Do this only once. It will remain set unless you change batteries or have otherwise
set DiagnosticOff. With DiagnosticOn, the correlation coefficient will also be shown
when a regression is performed.
2nd-CATALOG press "D" down arrow to "DiagnosticOn"
ENTER ENTER
Linear Regression
Enter the data into two lists.
Clear Y1 if you wish to save the regression equation: Y1= CLEAR
Perform the regression
STAT cursor to CALC "4:LinReg(ax+b)" or "8:LinReg(a+bx)"
(do not choose "9:LnReg")
2ND-LIST select list ENTER
, (comma) select list
optional: to store equation
, (comma) VARS
cursor to Y-VARS "1:Function"
cursor to the function desired ENTER
ENTER
Remember to turn off the plot of the regression line in the Y= menu prior to showing any other
statistical plots.
Creating a scatterplot with regression line
make the scatterplot in PLOT1 as above. If regression seems appropriate, continue.
Perform the regression, but augment the commands stated above for a regression as follows.
STAT cursor to CALC "8:LinReg(a+bx)"
2ND-LIST select list ENTER
, (comma) select list
, (comma) VARS
cursor to Y-VARS "1:Function"
ENTER to select Y1
ENTER
Now GRAPH.
Find a confidence interval for 1-sample or 2-sample mean(s)
For means, either we have raw data or we have summary statistics. If we have data, enter it into a list or 2 lists,
as is appropriate.
STAT TESTS cursor down to
the appropriate line; use 8 for a single mean, 0 for independent means. ENTER.
(7 and 9 assume you know σ(s). You could choose that and enter the sample std dev value(s) for &sigma to
approximate what we would do by hand if we use a z-distribution for large samples.)
If you have data for 1 mean or 2 means, choose "Data", select the list(s).
If you have summary statistics, choose "Stats" and enter the values.
Enter the confidence level. For 2 means, choose "No" for
Pooled (for our text.) "Calculate" and ENTER.
You will see the confidence interval. For a t-test, you will see df.
Perform a hypothesis test for 1-sample or 2-sample mean(s)
Either we have raw data or we have summary statistics. If we have data, enter it into a list or 2 lists,
as is appropriate.
STAT TESTS cursor down to
the appropriate line; use 2 for a single mean, 4 for independent means with a t-distribution. ENTER.
(1 and 3 assume you know σ(s). You could choose that and enter the sample std dev value(s) for &sigma to
approximate what we would do by hand if we use a z-distribution for large samples.)
If you have data for 1 mean or 2 means, choose "Data", select the list(s).
If you have summary statistics, choose "Stats" and enter the values.
Enter the hypothesized value. Select the appropriate alternative hypothesis. For 2 means, choose "No" for
Pooled (for our text.) "Calculate" and ENTER.
You will see the value of the test statistic and the p-value. For a t-test, you will see df.
If you wish to see the shaded area beyond the test statistic value for the alternative hypothesis that you chose,
STAT/TESTS/ etc. as before but select DRAW instead of calculate.
This also shows the test statistic value and a rounded p-value.
Find a confidence interval for 1-sample or 2-sample proportion(s)
For means, either we have raw data or we have summary statistics. If we have data, enter it into a list or 2 lists,
as is appropriate.
STAT TESTS cursor down to
the appropriate line; use 8 for a single mean, 0 for independent means;
Cursor down to A for a single proportion, B for two proportions. ENTER.
The "x" value(s) are the number of "successes". For instance, if our sample indicates that 25 out of 200 surveyed
love chocolate, then the sample proportion, p-hat, is .00125, but "x" is 25. If you are given n and p-hat, then x is
the product of n and p-hat.
Enter the confidence level. "Calculate" and ENTER.
You will see the confidence interval.
Perform a hypothesis test for 1-sample or 2-sample proportion(s)
Either we have raw data or we have summary statistics. If we have data, enter it into a list or 2 lists,
as is appropriate.
STAT TESTS cursor down to
the appropriate line; use 5 for a single proportion, 6 for two proportions. ENTER.
Enter the hypothesized value for a single proportion.
Select the appropriate alternative hypothesis.
The "x" value(s) are the number of "successes". For instance, if our sample indicates that 25 out of 200 surveyed
love chocolate, then the sample proportion, p-hat, is .00125, but "x" is 25. If you are given n and p-hat, then x is
the product of n and p-hat.
"Calculate" and ENTER.
You will see the value of the test statistic and the p-value.
If you wish to see the shaded area beyond the test statistic value for the alternative hypothesis that you chose,
STAT/TESTS/ etc. as before but select DRAW instead of calculate.
This also shows the test statistic value and a rounded p-value.
Entering data into a matrix
We do this before performing a chi-square test.
2nd-MATRIX EDIT choose the matrix
name, such as [A]. ENTER
type the number of rows; ENTER type the number of columns ENTER.
enter all of the values in the contingency table.
Perform a chi-square test
Enter the counts (absolute frequencies) of the table into a matrix, as above; it is easiest to use [A].
STAT cursor to TESTS cursor down to
"C: χ2-Test..." ENTER.
(If you used matrix [A], just) cursor down to "Calculate" and ENTER. Expected values will be in Matrix [B].
See the p-value and the df.
If you wish to see the shaded area past the test statistic value, STAT/TESTS/"C: χ2-Test...", DRAW.
This also shows the test statistic value and a rounded p-value.