Category Archives: TI-84

LU decomposition in TI-84

As an extension to a previous entry on doing LU decomposition in Nspire and R, the TI-84 is covered here. There is no built-in function like in the Nspire for this, but there are many programs available online, with most of them employing a simple Doolittle algorithm without pivoting.

The non-pivoting program described here for the TI-84 series is with a twist. No separate L and U matrix variables are used and the calculations are done in place with the original input matrix A. The end result of both L and U are also stored in this input matrix. This is made possible by the property of the L and U matrices in this decomposition are triangular. Therefore, at the little price of some mental interpretation of the program output, this program will take up less memory and run a little faster than most simple LU decomposition programs online for the same class of calculator. From a simple benchmark with a 5 x 5 matrix, this program took 2 seconds while another standard program took 2.7 seconds.

The input matrix A.

Results are stored in the same matrix.

L, U, and verification.

Durbin-Watson statistic in TI-84

Unlike the more sophisticated TI-89 and Nspire, the Durbin-Watson statistic is not included in the TI-84. Yet, calculating it is fairly straight-forward using list functions.

This statistics of regression is given as


where e is the residual list of values. To obtain this list (using a previous multiple regression example), simply subtract the actual values from the regression formula (Y7 below):

durbinwatson1 durbinwatson2

Finally, run the formula below for answer.


Graphical visualization of data distribution in TI-84 and R

For visualizing data distribution, the TI-84 Stat plot can provide some insights. Using the same data set as in the previous installment on Shapiro-Wilk test, TI-84 Stat plot is a quick and convenient tool.

shapiro84-graphplot2 shapiro84-graphplot1

In R, the command qqnorm() will show the following plot for the same data.


P value of Shapiro-Wilk test on TI-84

In previous installment, the Shapiro-Wilk test is performed step by step on the TI-84.

To calculate the p-value from this W statistic obtained, the following steps can also be done on the TI-84 using some standard statistics function. Note that the approximation below are for the case 4 ≤ n ≤ 11.

The mean and standard deviation are derived using the below equations.

The W statistic is assigned from the correlation calculation results, and another variable V is calculated for the transformed W.

Finally, the standardized Z statistic and p-value is calculated using the mean, standard deviation, and the transformed W value.
shapiro84-pvalue3 shapiro84-pvalue4

Micro SD card performance with different adaptor

There are several way to connect a micro SD card to a PC. The most popular being a versatile USB card reader that is capable to read different storage media. There are also built-in card reader on notebook computer.

Since the Android phone supported USB external media via OTG interface, there is a new kind of micro SD adapter on the market that work with both mobile device and PC, and are made very compact like the one on the right below.


To compare whether there will be difference in access speed, a simple test is performed using CrystalDiskMark with the two adapter devices above. Three groups of 10 sample read data (an internal SD reader of a notebook computer, a standard USB interface, and a USB 3.0 interface) are collected for the same micro-SD card which is a SanDisk 32GB class 4. The data are analysed using the ANOVA function available on the TI-84.

Looking at the p-value, there is a significant difference between any of the mean reading speed.

Moving average calculation on scientific vs financial calculator

The idea behind moving average is very simple. It used to be quite cumbersome for older generations of calculator to do this sort of calculation. With modern models, this is a piece of cake as the List feature is almost becoming a standard feature.

For the popular TI-84 series, the list feature can be used to store values into variables. Not only can the list be named, the name assigned can also consist of multiple characters. With the list defined, the moving averages can easily be calculated with arbitrary parameters.


On the financial model arena, the HP17bII+ is a special breed alongside its popular and successful line of signature financial calculator HP12c. The manual for the 17b provided an example that make use of the built-in solver for this. The menu driven 17b is quite convenient to use.