BrownMath.com→TI-83/84/89→SampleStatistics

Updated20Jan2021(What’sNew?)

Copyright © 2007–2023 by StanBrown, BrownMath.com

**Summary:**You can use your TI-83/84 to find**measures of central tendency and measures of dispersion**for a sample.

**Contents:**

- Descriptive Statistics for a List of Numbers
- Step 1: Enter the numbers in L1.
- Step 2: Compute the statistics.
- Step 3: Find the variance.

- Descriptive Statistics for a Frequency Distribution
- Step 1: Enter class marks in L1 and frequencies in L2.
- Step 2: Compute the statistics.
- Step 3: Find the variance.

- What’s New?

**Seealso:**MATH200A Program— Basic Statistics Utilities forTI-83/84 gives a downloadable programto plot histograms and box-whisker diagrams.

**Seealso:**optional advanced material: MATH200B Program part1gives a downloadable program that computes skewness and kurtosis, twonumerical measures of shape

## Descriptive Statistics for a List of Numbers

Quiz scores in a (fictitious) class were10.5, 13.5, 8, 12, 11.3, 9, 9.5, 5,15, 2.5, 10.5, 7, 11.5, 10, and 10.5.It’s hard to get much of a senseof the class by just staring at the numbers, butyou can easily compute the common measures of center and spread byusing your TI-83 or TI-84.

### Step 1: Enter the numbers in L1.

By the way, this note uses list L1, but you can actually use anylist you like, as long as you enter the actual list name in the`1-VarStats`

command in Step 2.(It doesn’t matter whether there are numbers in any other list.)

Enter the data points. | [`STAT` ] [`1` ] selects the list-edit screen. Cursor onto the label `L1` at top of first column, then [`CLEAR` ] [`ENTER` ] erases the list. Enter the x values. |

### Step 2: Compute the statistics.

Select the `1-VarStats` command. | [`STAT` ] [`►` ] [`1` ] pastes the command to the home screen. |

Specify which statistics list contains the data set. Show your work: write down `1-VarStats` and the list name. | Assuming you used `L1` , enter [`2nd` `1` makes `L1` ]. Press [ `ENTER` ] to execute the command. |

The important statistics are

**sample size***n*=15

Always check this first to guard against leaving out numbers orentering numbers twice.**mean***x̅*=9.72

(Write down symbol μ instead of*x̅*if this is a population mean.)**standard deviation***s*=3.17

Since this data set is a sample, use`Sx`

and write*s*for thestandard deviation. (When the data set is the whole population, use`σx`

and write σ for the standard deviation.)

If rounding is necessary, remember that we**round mean and standard deviation to one decimal place more than the data.****variance**is not shown on this screen; seeStep 3 below.

The down arrow on the screen tells you that there’s more information if you scroll down— in this case it’s the five-number summary. | [`▼` 5times ] for the five-number summary. |

You can tell the shape of the distribution. Sincethe mean *x̅*= 9.72 is just a hair less than the median`Med`

or *x̃*= 10.5, you know that the distribution is**slightly skewed left**.

The **range** is`Xmax`

− `Xmin`

= 15− 2.5=12.5.

The **interquartile range or IQR**is `Q3`

− `Q1`

= 11.5− 8=3.5. Recallthat we use 1.5× IQR toclassify outliers: we call a data point an outlier if it’sat least that far below Q1 or above Q3.

In this case1.5× IQR= 1.5× 3.5=5.25,Q1− 5.25=2.75, and Q3+ 5.25=16.75,so we can say that any data points below 2.75 or above 16.75 areoutliers. (Making a box-whisker plot is easier: see MATH200A Program part2.)

### Step 3: Find the variance.

Your TI-83 or TI-84 doesn’t find the variance for youautomatically, but since the standard deviation is the square root ofthe variance, you can**find the variance by squaring the standard deviation.**

It would be**wrong to compute s²= 3.17²**=10.05— see the Big No-no for thereason. You could enter 3.165257832², but that’s tedious anderror prone, as well as being overkill. Instead,

**use the value that the calculator has stored in a variable.**

Select statistics variables. | [`VARS` ] [`5` ] |

Select the correct standard deviation: `Sx` if your data set is a sample or `σx` if your data set is the whole population. | [`3` ] for `Sx` or [`4` ] for `σx` . |

Square it. The variance is s²=10.02. (If the data set was a whole population, you’d use σ² for the variance.) | [`x²` ] [`ENTER` ] |

## Descriptive Statistics for a Frequency Distribution

Class Boundaries | Class Marks | Frequency |
---|---|---|

20 ≤ x < 30 | 25 | 34 |

30 ≤ x < 40 | 35 | 58 |

40 ≤ x < 50 | 45 | 76 |

50 ≤ x < 60 | 55 | 187 |

60 ≤ x < 70 | 65 | 254 |

70 ≤ x < 80 | 75 | 241 |

80 ≤ x < 90 | 85 | 147 |

The grouped frequency distribution at right is the agesreported by Roman Catholic nuns, from [full citation at https://BrownMath.com/swt/sources.htm#so_Johnson2004], page 67.Let’s use the TI-83/84 to compute statistics.

### Step 1: Enter class marks in L1 and frequencies in L2.

By the way, this note uses L1 and L2, but you can use anylists you like, as long as you enter the actual list names in the`1-VarStats`

command in Step 2.(It doesn’t matter whether there are numbers in any other list.)

This example is for a grouped frequency distribution. If youhave an **ungrouped frequency distribution**, you can computestatistics in the same way. The only difference is that your firstlist will contain the actual values instead of the class marks.

Enter the class marks in `L1` . (The class mark is the midpoint of each class.) | [`STAT` ] [`1` ] selects the list-edit screen. Cursor onto the label `L1` at top of first column, then [`CLEAR` ] [`ENTER` ] erases the list. Enter the class marks. (If you have only the class boundaries, you can make the TI-83/84 do the work for you. It will compute the class marks automatically if you enter the class boundaries in the form `(20+30)÷2` .) |

Enter the frequencies in `L2` . | Cursor onto the label `L2` at top of first column, then [`CLEAR` ] [`ENTER` ] erases the list. Enter the frequencies. |

### Step 2: Compute the statistics.

Select the `1-VarStats` command. | [`STAT` ] [`►` ] [`1` ] pastes the command to the home screen. |

Specify which statistics lists contain the data set and the frequencies, in that order. Show your work: write down `1-VarStats` and both lists. Important: You must supply both lists. That’s the only way the calculator knows you have a frequency distribution. Always check the sample size n in the output, to guard against forgetting to enter the second list. If you see n is the number of classes instead of the number of data points, redo your `1-VarStats` and this time specify both lists. | Assuming you used `L1` and `L2` , enter [`2nd` `1` makes `L1` ] [`,` ] [`2nd` `2` makes `L2` ]. Press [ `ENTER` ] to execute the command. |

The important statistics are

**sample size***n*=997

Again, if this is a low number it means you forgot to specifyfrequencies on the`1-Var Stats`

command.**mean***x̅*=63.9

(Write symbol μ if this is a population mean.)**standard deviation***s*=15.4

If this data set is a sample, use`Sx`

and write*s*for thestandard deviation; if this data set is the whole population(including a probability distribution), use`σx`

and write σ for the standard deviation.**variance**is not shown on this screen; seeStep 3 below.

Remember that **the values on this screen are approximate**because the frequency distribution is an approximation of the originalraw data. For most real-life data sets, the approximation isquite good, and it is very good for moderate to large data sets.

The down arrow on the screen tells you that there’smore information if you scroll down. However, since the numbers youenter in a grouped frequency distribution are only approximate,the five-number summary is only approximate. The Min and Maxare just the highest and lowest classes. Q1, Med, and Q3 are at bestthe midpoints of the classes that actually contain thosestatistics.

As a general rule, **the five-number summary from a grouped frequency distribution is not worth reporting.**The numbers will be only approximations, becausethe calculator has only the class midpoints to work with and not theoriginal data.

### Step 3: Find the variance.

Just as with a simple list of numbers, you**find the variance by squaring the standard deviation.**

It would be**wrong to compute s²= 15.4²**=237.2— see the Big No-no for the reason.Instead, use the value that the calculator has stored in avariable.

Select statistics variables. | [`VARS` ] [`5` ] |

Select the correct standard deviation: `Sx` if your data set is a sample or `σx` if your data set is the whole population. | [`3` ] for `Sx` or [`4` ] for`σx` . |

Square it. The variance is s²=238.2. (If the data set was a whole population, the variance would be σ².) | [`x²` ] [`ENTER` ] |

## What’s New?

**20 Jan 2021**: In response to a reader’s query, clarifiedthe choice between`Sx`

and`σx`

, here and here.**9 Nov 2020**: Converted from HTML 4.01 to HTML5. Made a adozen or so small edits for clarity. Formatted math variable names andnames of variables seen on TI screens.- (Intervening changes suppressed.)
**6 Sep 2007**: New article.

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## FAQs

### Is a TI 83 good for statistics? ›

**It has a wide range of features that make it ideal for statistics courses**. The TI-83 Plus has built-in functions for statistical analysis, including regression, hypothesis testing, and data analysis.

**How do you find the sample statistic on a TI-84? ›**

- Step 1: Enter the Data. First, we will enter the data values. Press Stat, then press EDIT. Then enter the values of the sample in column L1: ...
- Step 2: Find the Sample Variance. Next, press Stat and then scroll over to the right and press CALC. Then press 1-Var Stats. In the new screen that appears, press Enter.

**Can I use a TI-84 for statistics? ›**

TI-84: CALCULATING SUMMARY STATISTICS

**Use the STAT, CALC, 1-Var Stats command to find summary statistics such as mean, standard deviation, and quartiles**.

**Which TI calculator is best for statistics? ›**

**Top 5 Best Calculators For Statistics (2022)**

- Texas Instruments TI-36X Pro Engineering/Scientific Calculator.
- CATIGA CS-121 Scientific Calculator with Graphic Functions.
- Casio FX-991EX Engineering/Scientific Calculator.
- Sharp Calculators EL-W535TGBBL 16-Digit Scientific Calculator with WriteView.
- Mr.

**Is TI-83 outdated? ›**

**Technology has not yet killed the reliable old TI-83**. Nearly 20 years later, students are still forced to use a prohibitively expensive piece of outdated technology. It's not because better tools aren't available; they exist, and some of them are even free.

**How do you find the sample mean on a TI 83? ›**

**Once you're in the CALC menu, select 2-Var Stats**. (If we had only entered a single column of data, 1-Var Stats would be the appropriate choice instead.) Then hit ENTER. The calculator will display the x-mean (= 2.5), some other stuff, and then the standard deviation (s_{x}=1.29).

**How do you find a sample statistic? ›**

**How to calculate the sample mean**

- Add up the sample items. First, you will need to count how many sample items you have within a data set and add up the total amount of items. ...
- Divide sum by the number of samples. ...
- The result is the mean. ...
- Use the mean to find the variance. ...
- Use the variance to find the standard deviation.

**Why do I get different answers in calculator? ›**

**Each calculator may have a different algorithm for calculating the answer**. Each calculator may be programed to calculate a different degree of accuracy. Each calculator may have a different number of digits it can display.

**How do calculators know the answer so fast? ›**

Calculators (and computers) **combine inputs using electronic components called logic gates**. As the name implies, a logic gate acts as a barrier in an electronic circuit; it takes in two electric currents, compares them and sends out a new current based on what it finds.

**How do calculators have all the answers? ›**

**The memory chips inside the calculator contain thousands or millions of bytes of program code that allows the calculator to do the work**. In some cases, the chips may contain some information in table form, while in others, they contain sequences of steps that can be used to get to the answer.

### Can you use a TI-84 in college? ›

**Yes, in many instances teachers allow students to use TI graphing calculators on class tests**. In fact, graphing calculators are permitted, or even required, on many college entrance exams and state exams.

**What is the strongest TI calculator? ›**

The **HP Prime G2** is the best HP currently. The HP-50g has been the professional engineer's go to for decades, and you can still find them online. The HP35s is the only programmable scientific calculator allowed on Professional Engineering exams.

**Why is the TI-83 still so expensive? ›**

A TI-83 will set a student back around $100, while the TI-84 still costs more than $100. Most obsolete gadgets lower in price (consider this $10 flip-phone), but the humble graphing calculator continues to boast a hefty price tag. What gives? **It's all about supply and demand**.

**Is TI-83 or 84 better? ›**

In the real world this makes the **TI-84 Plus about 2x as fast as the TI-83 Plus**. The TI-83 also has 160 KB of storage whereas the TI-84 Plus has 480 KB. Both calculators have the same 24 KB of RAM. The main software difference is that the TI-84 Plus is that the TI-84 Plus has MATHPRINT and the TI-83 doesn't.

**How long does a TI-83 calculator last? ›**

The four AAA bat- teries in the calculator usually last for **about a year** with normal use in a calculus course. The backup battery can last anywhere from 2 to 5 years.

**What does a TI 83 calculator do? ›**

Easy-to-use graphing calculator for math and science that **lets students graph and compare functions, as well as perform data plotting and analysis**. Its Flash™ ROM memory allows students to update and add software applications (apps).

**How do you find the summary statistics on a TI 83? ›**

**HOW TO FIND THE FIVE–NUMBER SUMMARY, VARIANCE AND STANDARD DEVIATION WITH TI83 CALCULATOR**

- Enter data into list, L
_{1} - Select 1–Var Stats. STAT. once. ...
- Select the list, L
_{1}2^{nd}then 1. - Find the Statistics. ENTER. * is the mean * Sx is the sample standard deviation * σx is the population standard deviation.
- Find the 5-number summary.

**Can the TI-83 Plus do financial calculations? ›**

TI-83 Plus or TI-84 Plus, **press APPS and then 1:Finance.** **Once you are at the finance menu, select 1:TVM Solver**. – I% = interest rate (as a percentage) – PV = present value – PMT = payment amount (0 for this class) – FV =future value – P/Y = C/Y =the number of compounding periods per year.

**Can you do standard deviation on a TI-84? ›**

**Standard deviation can be calculated using several methods on the TI-83 Plus and TI-84 Plus Family**. Standard deviation can be calculated by using the stdDev() function.

**What is a sample test statistic? ›**

A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.

### What is the sample and sample statistic? ›

**A sample statistic is a figure that is computed from a sample of data**. A sample is a piece or set of objects taken from a statistical population. In other words, a sample statistic is just a calculation taken from a sample that is just a piece of a population.

**Why do we need sample statistics? ›**

In statistics, a sample is an analytic subset of a larger population. The use of samples **allows researchers to conduct their studies with more manageable data and in a timely manner**. Randomly drawn samples do not have much bias if they are large enough, but achieving such a sample may be expensive and time-consuming.

**How do you turn off the trick on a calculator? ›**

**Press and hold ON, C/CE, or AC for a moment while holding the keys above**. With the right combination of keys above, this should shut off the calculator.

**Can a calculator make a mistake? ›**

**Yes, calculators can be wrong**. They are nothing but simple computers and as such are only as good as their coding and will always have some limitations involving for instance rounding. Some errors can be avoided by paying attention to how you enter a problem if you are aware of the flaw in the coding.

**Can calculator sometimes be wrong? ›**

Calculators are often unnecessary to solve routine problems, though they are convenient for offloading cognitively effortful processes. However, **errors can arise if incorrect procedures are used or when users fail to monitor the output for keystroke mistakes**.

**Who is the fastest math calculator? ›**

Did you know that the "World's Fastest Human Calculator", a title that you're probably hearing for the first time, is an Indian man? Born in Andhra Pradesh's Eluru in 1999, Neelakantha Bhanu Prakash "is to math what Usain Bolt is to running," at least according to the BBC.

**What makes a calculator so smart? ›**

**Integrated circuits contain transistors that can be turned on and off with electricity to perform mathematical calculations**. The most basic calculations are addition, subtraction, multiplication, and division. The more transistors an integrated circuit has, the more advanced mathematical functions it can perform.

**Which scientific calculator has the most functions? ›**

**Casio FX-991EX**

There is a faster processor and double the memory size of the classic FX-ES Plus series. There are 522 functions, allowing you to work through large spreadsheets and matrix calculations.

**Do calculators run out of battery? ›**

**When properly maintained and under normal usage, batteries are expected to last about 3 years**. If you use the handheld/graphing calculator regularly, recharge the battery often. Avoid waiting until it is fully discharged.

**Do calculators produce knowledge? ›**

not be stimulated or challenged enough. Calculators do only the low level tasks of computation - they do not “think.” Calculators can speed up the learning process. Students understanding the appropriate use of calculators experience more time to explore challenging and interesting mathematics.

### Can a TI-84 solve algebra? ›

In addition to trigonometric functions, exponents, cube roots, matrices and of course graphs, **you can use the TI-84 to solve simple algebraic equations with the Solver option of the Math menu**.

**Why is a TI-84 calculator so expensive? ›**

**Limited Market Competition**. Graphing calculators are expensive because of limited competition in the market. Only a few brands, such as Texas Instruments, Casio, and HP, dominate the market, giving them the power to charge premium prices.

**Is there a difference between TI-84 and TI-84 Plus? ›**

**The TI-84 CE Plus is the latest in a long line of TI-84 calculators, but with a better color screen, battery life, software, and a more compact size**. It is the most widely adopted, widely trusted calculator by teachers in American classrooms.

**What calculator do most college students use? ›**

**Best Calculators for College Students**

- Texas Instruments TI-84 Plus CE Graphing Calculator.
- Casio FX-991EX Engineering/Scientific Calculator.
- Sharp EL-W516TBSL 16 Digit Advanced Scientific Calculator.
- Texas Instrument TI-30XS MultiView Scientific Calculator.

**Why do colleges not allow graphing calculators? ›**

One major concern is cheating. **People can enter information into their calculators that may give them an unfair advantage on the exam**, in essence using the calculator as a "cheat sheet". Having a professor verify that a couple hundred students don't have any information stored in their calculators isn't feasible.

**How to do a test statistic on TI-84? ›**

**How do I compute a T-Test on the TI-83 Plus and TI-84 Plus Family of graphing calculators?**

- Press [STAT] [1] to access the STAT List Editor.
- Input the example data into the L1 list, pressing the [ENTER] key after each entry.
- Press [2nd] [MODE] to QUIT the STAT List Editor and return to the home screen.

**What is the easiest way to sample randomly? ›**

This can be done in one of two ways: **the lottery or random number method**. In the lottery method, you choose the sample at random by “drawing from a hat” or by using a computer program that will simulate the same action. In the random number method, you assign every individual a number.

**How to do statistics on a TI-83? ›**

To enter data, press STAT and go to 1:EDIT • In the first empty column, enter the data for variable 1 • Move the cursor to column L2, and enter the second variable's data in that column • Press STAT, and then move cursor to CALC. Press 2:2-Var Stats • Select the variables for which you wish to do the computation.

**What is a TI-83 Plus calculator used for? ›**

Easy-to-use graphing calculator for math and science that **lets students graph and compare functions, as well as perform data plotting and analysis**. Its Flash™ ROM memory allows students to update and add software applications (apps).

**Can I use a TI-83 on the PSAT? ›**

Scientific calculator: **The PSAT allows the use of any scientific calculator**.

### Why are TI-83 still expensive? ›

A TI-83 will set a student back around $100, while the TI-84 still costs more than $100. Most obsolete gadgets lower in price (consider this $10 flip-phone), but the humble graphing calculator continues to boast a hefty price tag. What gives? **It's all about supply and demand**.

**What's the difference between TI-83 and TI-83 Plus? ›**

TI-83 Plus

A link port is also built into the calculator in the form of a 2.5mm jack. **The main improvement over the TI-83, however, is the addition of 512 KB of Flash ROM**, which allows for operating system upgrades and applications to be installed.

**What calculators are not allowed on PSAT? ›**

**Prohibited Calculators**

- Laptops or other computers, tablets, mobile phones, smartwatches, or wearable technology.
- Models that can access the Internet, have wireless, Bluetooth, cellular, audio/video recording and playing, camera, or any other smartphone-type features.

**What is an OK score on the PSAT? ›**

The average PSAT/NMSQT score is about 920. A score **between 1210 and 1520** puts you in the top 10% of test takers. The PSAT/NMSQT and the SAT are very similar tests, so your score on the PSAT/NMSQT can give you an idea of how you'll do when you take the SAT.

**What PSAT score is equivalent to SAT? ›**

PSAT scores are placed on the same scale as SAT scores. The idea is that **a 650 on the PSAT represents the same achievement as a 650 on the SAT**. To the extent that PSAT and SAT scores can be used interchangeably, they can also share a concordance.

**Is the TI-84 outdated? ›**

Texas Instrument's best-selling graphing calculator, the TI-84, is **a woefully outdated piece of technology**. Since its debut in 2004, its specs and components have remained virtually unchanged.

**How old is the TI-83 Plus? ›**

Model | Release Date |
---|---|

TI-73 | July 1998 |

TI-89 | October 1998 |

TI-83 Plus | April 1999 |

TI-83 Plus Silver Edition | January 2001 |

**Can a TI-83 be used as a financial calculator? ›**

**The TI 83 (TI 83 Plus) is a fairly easy, but more difficult than most, to use financial calculator** which will serve you well in all finance courses. This tutorial will demonstrate how to use the financial functions to handle basic time value of money problems.