# Statistical Calculations

## Find Out The Sample Size

This calculator computes the minimum number of necessary samples to meet the desired statistical constraints.

- Excel provides an extensive range of Statistical Functions, that perform calculations from basic mean, median & mode to the more complex statistical distribution and probability tests. The Excel Statistical functions are all listed in the tables below, grouped into categories, to help you to.
- Two Sample Confidence Intervals and Tests of Hypotheses Difference of Proportions ( )pp 12− 12 12 12 11 2 2 /2 12 1 1 1 2 2 2 1 12 2 12 12 12 Confidence Interval.
- The calculator has established itself as a must-have and can-do-without for students and professionals, including organizations enaging in statistics. Individual choice of a statistics calculator depends on various factors, including purpose intended, screen display, versatility, built-in function, durability, cost, mode of operations, unique features, and keys.

The dice probability calculator is a great tool if you want to estimate the dice roll probability over numerous variants. There are may different polyhedral die included, so you can explore the probability of a 20 sided die as well as that of a regular cubic die.

## Find Out the Margin of Error

This calculator gives out the margin of error or confidence interval of an observation or survey.

### Statistical Calculations Are Extensively Done With

In statistics, information is often inferred about a population by studying a finite number of individuals from that population, i.e. the population is sampled, and it is assumed that characteristics of the sample are representative of the overall population. For the following, it is assumed that there is a population of individuals where some proportion, **p**, of the population is distinguishable from the other **1-p** in some way; e.g. **p** may be the proportion of individuals who have brown hair, while the remaining **1-p** have black, blond, red, etc. Thus, to estimate **p** in the population, a sample of **n** individuals could be taken from the population, and the sample proportion, **p̂**, calculated for sampled individuals who have brown hair. Unfortunately, unless the full population is sampled, the estimate **p̂** most likely won't equal the true value **p**, since **p̂** suffers from sampling noise, i.e. it depends on the particular individuals that were sampled. However, sampling statistics can be used to calculate what are called confidence intervals, which are an indication of how close the estimate **p̂** is to the true value **p**.

### Statistics of a Random Sample

The uncertainty in a given random sample (namely that is expected that the proportion estimate, **p̂**, is a good, but not perfect, approximation for the true proportion **p**) can be summarized by saying that the estimate **p̂** is normally distributed with mean **p** and variance **p(1-p)/n**. For an explanation of why the sample estimate is normally distributed, study the Central Limit Theorem. As defined below, confidence level, confidence intervals, and sample sizes are all calculated with respect to this sampling distribution. In short, the confidence interval gives an interval around **p** in which an estimate **p̂** is 'likely' to be. The confidence level gives just how 'likely' this is – e.g. a 95% confidence level indicates that it is expected that an estimate **p̂** lies in the confidence interval for 95% of the random samples that could be taken. The confidence interval depends on the sample size, **n** (the variance of the sample distribution is inversely proportional to **n** meaning that the estimate gets closer to the true proportion as **n** increases); thus, an acceptable error rate in the estimate can also be set, called the margin of error, **ε**, and solved for the sample size required for the chosen confidence interval to be smaller than **e**; a calculation known as 'sample size calculation.'

### Confidence Level

The confidence level is a measure of certainty regarding how accurately a sample reflects the population being studied within a chosen confidence interval. The most commonly used confidence levels are 90%, 95%, and 99% which each have their own corresponding z-scores (which can be found using an equation or widely available tables like the one provided below) based on the chosen confidence level. Note that using z-scores assumes that the sampling distribution is normally distributed, as described above in 'Statistics of a Random Sample.' Given that an experiment or survey is repeated many times, the confidence level essentially indicates the percentage of the time that the resulting interval found from repeated tests will contain the true result.

Confidence Level | z-score (±) |

0.70 | 1.04 |

0.75 | 1.15 |

0.80 | 1.28 |

0.85 | 1.44 |

0.92 | 1.75 |

0.95 | 1.96 |

0.96 | 2.05 |

0.98 | 2.33 |

0.99 | 2.58 |

0.999 | 3.29 |

0.9999 | 3.89 |

0.99999 | 4.42 |

### Confidence Interval

In statistics, a confidence interval is an estimated range of likely values for a population parameter, for example 40 ± 2 or 40 ± 5%. Taking the commonly used 95% confidence level as an example, if the same population were sampled multiple times, and interval estimates made on each occasion, in approximately 95% of the cases, the true population parameter would be contained within the interval. Note that the 95% probability refers to the reliability of the estimation procedure and not to a specific interval. Once an interval is calculated, it either contains or does not contain the population parameter of interest. Some factors that affect the width of a confidence interval include: size of the sample, confidence level, and variability within the sample.

There are different equations that can be used to calculate confidence intervals depending on factors such as whether the standard deviation is known or smaller samples (n<30) are involved, among others. The calculator provided on this page calculates the confidence interval for a proportion and uses the following equations:

where z is z scorep̂ is the population proportionn and n' are sample sizeN is population size |

Within statistics, a population is a set of events or elements that have some relevance regarding a given question or experiment. It can refer to an existing group of objects, systems, or even a hypothetical group of objects. Most commonly however, population is used to refer to a group of people, whether they are the number of employees in a company, number of people within a certain age group of some geographic area, or number of students in a university's library at any given time.

It is important to note that the equation needs to be adjusted when considering a finite population, as shown above. The **(N-n)/(N-1)** term in the finite population equation is referred to as the finite population correction factor, and is necessary because it cannot be assumed that all individuals in a sample are independent. For example, if the study population involves 10 people in a room with ages ranging from 1 to 100, and one of those chosen has an age of 100, the next person chosen is more likely to have a lower age. The finite population correction factor accounts for factors such as these. Refer below for an example of calculating a confidence interval with an unlimited population.

EX: Given that 120 people work at Company Q, 85 of which drink coffee daily, find the 99% confidence interval of the true proportion of people who drink coffee at Company Q on a daily basis.

### Sample Size Calculation

Sample size is a statistical concept that involves determining the number of observations or replicates (the repetition of an experimental condition used to estimate variability of a phenomenon) that should be included in a statistical sample. It is an important aspect of any empirical study requiring that inferences be made about a population based on a sample. Essentially, sample sizes are used to represent parts of a population chosen for any given survey or experiment. To carry out this calculation, set the margin of error, **ε**, or the maximum distance desired for the sample estimate to deviate from the true value. To do this, use the confidence interval equation above, but set the term to the right of the ± sign equal to the margin of error, and solve for the resulting equation for sample size, **n**. The equation for calculating sample size is shown below.

where z is the z scoreε is the margin of errorN is population sizep̂ is the population proportion |

EX: Determine the sample size necessary to estimate the proportion of people shopping at a supermarket in the US that identify as vegan with 95% confidence, and a margin of error of 5%. Assume a population proportion of 0.5, and unlimited population size. Remember that **z** for a 95% confidence level is 1.96. Refer to the table provided in the confidence level section for **z** scores of a range of confidence levels.

Thus, for the case above, a sample size of at least 385 people would be necessary. In the above example, some studies estimate that approximately 6% of the US population identify as vegan, so rather than assuming 0.5 for **p̂**, 0.06 would be used. If it was known that 40 out of 500 people that entered a particular supermarket on a given day were vegan, **p̂** would then be 0.08.

**Finding The Best Calculator For Statistics on The Market**

The best calculator for statistics has always been a conundrum among students. On the one hand, you have teachers who recommend getting a graphing calculator and on the other, experts on internet forums recommending better and more advanced programs like R or STATA in place of a calculator.

To buy or not to buy, that is the question. And the fact that statistical calculators aren’t cheap makes it an important question, since for many it will represent a substantial investment. The fact is, almost every student who has ever studied statistics has owned a calculator, going all the way back to the granddaddy of them all, the TI-83, which was arguably the most popular statistical calculator for two decades. Talk to anyone who used the TI-83 calculator and probably they’ll not only still own it, but claim it still works like a charm too.

**How Do I Choose?**

The market isn’t limited to the TI-83s anymore. It has exploded with options and a lot of these are cheaply made Chinese imports that may or may not work right out of the box. This makes it very important to tread carefully while buying one of these, lest you are ok being swindled out of almost $100-$150.

As a helping hand to the students who are new to this process and looking for some unbiased guidance, we’ve compiled a list of the top five statistical calculators on the market. In our opinion, the best calculator for statistics class is one that offers the best balance of advanced features, durable construction, and affordability. Whether you want the best non programmable calculator or one with all the bells and whistles we’ve got it covered. These calculators have been handpicked based on an exhaustive analysis of performance, price and customer reviews. None of them are a bad choice, but hopefully this guide will help you pinpoint the calculator that is most conducive to your needs. Without further ado:

**1 – HP G8X92AA LA Prime v2**

****[Editor Top Pick]****

The G8X92AA from HP is a cutting-edge new generation statistical calculator that boasts of features like a full-color display, multi touch control options like the keyboard or the touch screen and the ability to switch between different types of views (Graphical or numbers) with dedicated keys.

That’s not all either. With a simple firmware upgrade and HP Prime Wireless Kit1 and HP Connectivity Kit, you also get support for P2P (Prime to Prime) and in-class Wi-Fi that allows you to wirelessly connect and transfer data between the calculator and a computer. As would be evident by now, the usage of the calculator is not limited to a statistic class. It is also widely used in engineering, chemistry, computer science, trigonometry and the likes.

**Sleek, Stylish With a Cover**

Unlike the other models that have remained unchanged over the years, the **HP G8X92AA** looks stylish and sleek. It has a brushed metal chassis with a matte-silver finish that not only looks good, it also adds to the durability of the unit. Accidentally dropped it while fiddling with the keys? It will work flawlessly.

Oh, by the way, it features a slide-on cover that will protect the keypad and the touch screen when it’s not in use. The keypad is quintessential HP and if you prefer going the touch screen way, then you will find that the 3.5 inch screen with multi diagonal touch allows you ample room to toggle through the menu and find the application you need.

**Packed To The Brim With Features**

The HP G8X92AA is hands down, the most feature rich statistic calculator that we have seen in recent times. There’s no end to what you can do with it. But just to give you an idea, it features graphing functions like scatter plot, 2-D, parametric and more, Scientific functions like unit conversions, Boolean graphics and angle conversions, statistical functions like Σx, Σx2, Σy, Σy2, Σxy, linear regression and more.

It is approved for use in PSAT/NMSQT®, SAT®, SAT® and select AP® Exams. What’s more is that a single button will activate a test mode during which only selected applications work, turning it into a mock test interface. The G8X92AA is powered by a rechargeable lithium ion battery that can be powered by direct power or by a USB connection.

**Best Features**

- Sleek and stylish metallic casing
- 5 inch multi touch LCD full-color display
- Loaded with apps and features
- Perfectly placed buttons on the Keypad
- Approved for use in PSAT/NMSQT®, SAT®, SAT® and select AP® Exams
- USB connectivity
- Support for P2P (Prime to Prime) and in-class Wi-Fi

**To Sum It Up**

If money is not a constraint and you are looking for an advanced statistical calculator, go for the HP G8X92AA.

**#2 – Casio fx-9750GII Graphing Calculator, White**

**[The Best statistics calculator for price]**

Casio was always the fastest growing competition for TI and the FX-9750GII which was their entry level model almost rivaled the TI-83 Plus in popularity. That has a lot to do with the under $50 price tag though. And as expected at this price point it is not loaded with bells and whistles. Instead, it has a barebones interface with just enough features that you’d need for your calculations and exams.

For some boasting rights, it was the 9750 series that first introduced the USB technology way back in 2009. While that may seem pale in comparison today, it pretty much sums up what the FX-9750GII stands for.

**Compact Sized Calculator**

At just about 6 inches in length, the FX-9750GII is more compact than other statistical calculators even from Casio. But the buttons are laid out in perfect logical order which makes it as easy to use as some of its higher priced brethren. If you have seen the 9860GII from Casio, you’d find that it almost looks like a smaller mirror image of that model. Occupying the center of the screen is a high-resolution LCD display with Casio’s proprietary enlarged dot-area technology which enables you to get really crisp and sharp graphs and formulas. The visibility is excellent even in a dimly-lit classroom and you should have no problems finding your way around the calculations.

**Fast And Inexpensive**

Powering the **Casio fx-9750GII** is an excellent CPU with 62KB RAM that allows a lag-free and fast performance even for the most complex calculations and graphs. During a test, this may well make the difference between completing the answers on time and wrecking your head over a calculator that takes ages to respond. It is compatible for use in PSAT/NMSQT, SAT, and ACT entrance exams and AP tests. The biggest draw of the Casio fx-9750GII though, remains the price tag. It is priced at almost half of what most statistical calculators cost. And at that price point, it isn’t a bad option at all.

**Best Features**

- Pocket-sized Casio statistical calculator
- Compatible for use in PSAT/NMSQT, SAT, and ACT exams and AP tests
- High speed CPU with 62KB RAM
- High-resolution LCD display with enlarged dot-area technology
- USB Connectivity

**To Sum It Up**

If you are looking for the best calculator for statistics on a budget, look no further. The Casio fx-9750GII is your best bet. It may not be the most advanced one in this list, but it more than suffices for use in school and college.

**#3 – Sharp EL-W535TGBBL 16-Digit Scientific Calculator with WriteView**

Talk about budget priced statistical calculators and no one would believe that you could buy one that’s priced under $15. And it isn’t one of those cheap Chinese-made gimcracks either. This is the Sharp EL-W535TGBBL that earns the reputation of being the cheapest statistical calculator in the market currently.

That moniker does not do justice to the device for this is an amazingly versatile calculator that can help you perform over 330 types of functions and calculations. That’s not bad at all. Club that with the reasonably large display and excellent keypad quality, you have a very worthy #3 choice in this list of the best stats calculators.

**Twin Power Calculator**

The Sharp EL-W535TGBBL is the only calculator in this list that can be powered by both batteries as well as solar power. While that does little to improve the lifespan of the calculator, it does assure you that if the battery runs out of juice at a crucial juncture, you still have the option to power the calculator for that little extra time. It is not the most compact one that we have seen. It is approximately 9 inches in length. But this gives you ample spaces between the keys on the keypad. The construction is pretty rugged too and the Sharp EL-W535TGBBL also comes with a slide-on cover protector.

**Writeview Technology**

Another neat addition to the list of features for the Sharp EL-W535TGBBL is the Writeview technology that displays formulas exactly as they appear in a textbook. This makes them easier to understand and solve rather than wasting time trying to figure out the formulas by drawing comparisons. The 4-line display is not top notch. But it does the job. Visibility is pretty good too. The calculator also features a playback function that allows you to go back and edit the formulas in case of an error. Along with the 335 function solving ability, it also allows users to solve up to three equations at the same time. User functions can be programmed into four programmable keys for easy and instant access.

**Best Features**

- Scientific and mathematical calculator priced under $15
- Up to 335 calculations
- Four line display
- Playback function for editing formulas
- Solve up to 3 equations at the same time
- WriteView technology that displays formulas the way they are shown in textbooks
- Slide-on cover protector
- Dual power source
- Approved for use in AP Chemistry, AP Physics, PSAT/NMSQT, SAT I, SAT II, Math IC, and Math IIC

**To Sum It Up**

The **Sharp EL-W535TGBBL** may not be the best calculator for statistics that money can buy. But if you are not looking for advanced features, then this might be a good choice for you. You should ideally speak to your high school teacher before you pick this. Many teachers prefer that their students either pick the TI-84 or the HP G8X92AA due to the ease of use.

**#4 – Texas Instruments TI-84 Plus Graphing Calculator**

We start our list of the best graphic calculators with what has been a worthy successor to the immensely popular TI-83. This is the TI-84 from Texas Instruments and it boasts of a whole laundry list of features that make life simpler in your calculations and during your tests.

The good thing about Texas Instruments statistical calculators is they’re reliable. This model is approved for use during most common tests like the AP and IB as well as during exams like the PSAT, SAT and ACT. For the uninitiated, the ACT restricts the use of calculators like the TI-89 Titanium or the TI-Nspire CX that have integrated algebra systems

**The Community Favorite**

Despite being around for over a decade and despite Texas Instruments coming up with a full colored version, the **TI-84 plus** with its black and white interface remains a favorite among both students as well as the entire mathematics community in general. It is widely used in schools and many of the schools have also invested in software programs and training modules that rely on the TI-84 for teachers.

One of the most important reasons for the popularity is the 2.55 MP operating system (upgraded from the 2.53 MP) that makes it immensely easy to use irrespective of whether you are using it for calculus or advanced algebra. Not to mention that it has the same elegant design with tactile buttons that are well spaced, which is always a plus.

**Versatile Features**

Along with the new operating system, the TI-84 has also gotten a bunch of new templates like summations, a bunch of quick access pop-up windows with dedicated keys to them and the ability to go back and alter previously made calculations which makes repetitive tasks a breeze. To top it off, there’s a huge list of applications included in the TI-84 like the Cabri Jr, Conic Graphing, Inequality Graphing, Simultaneous Equation solving, Probability Simulator, Vernier Easy Data and Polynomial Root Finder. Compatibility with USB allows you to back up and transfer data seamlessly between your computer and the TI-84.

**Best Features**

- Compact and elegant design
- Loaded with apps
- Dedicated keys for popup windows
- Lots of additional templates
- USB Compatibility to back up data
- Allowed for use during tests like AP, IB and exams like PSAT and NCT

**To Sum It Up**

It lacks the backlit color display and the crispness of the CE Plus. Also, there’s lesser scope of arranging a lot of data on the screen. But that’s not a deal breaker. With the versatility, the ease of use and the wide acceptance in the community, you won’t find a better and more reliable choice for the best calculator for statistics.

**#5 – Texas Instruments BA II Plus Financial Calculator**

We decided to end this list with the BA II Plus, probably the best calculator for college statistics. It’s slightly more advanced and offers financial calculations in addition to the standard mathematical functions. Along with an impressive feature bundle, it is also priced under $30.

The feature list is highlighted by a worksheet mode that lets you easily include tables for a variety of functions, a slide-on protective case for the keypad and in-built storage memory that allows you to store your worksheets.

**Multiple Modes**

If you are coming to the TI BA II Plus from a standard mathematical or statistical calculator, then you may find it a tad difficult to get used to the interface and the new functions. That’s partly because there are two different modes in which you can use this. The standard mode is easier to use and the other one is a worksheet mode.

While the standard mode lets you perform standard tasks along with finance related calculations like mortgage, annuities and trigonometry, the worksheet mode allows you to perform more advanced functions like amortization, depreciation and compound interest. With in-built storage, you can store your worksheets for later use and this prevents the need for typing cumbersome numbers all over again.

**Lightweight And Minimalistic**

At first glance, the BA II Plus looks very similar to the TI-83 in the design and the keypad layout. But it is smaller in size and lightweight too. It has a 16-digit LCD display that shows crisp and sharp numbers with excellent contrast. Also, we must mention the excellent user manual that accompanies the BA II Plus without which, it would be extremely difficult for a newbie to get to use the calculator. At a time when there’s a new model being launched every other day, TI’s BA II Plus has managed to hold its own and is currently the bestselling financial calculator on Amazon.

**Best Features**

- Priced under $30
- Large 16 digit display
- In-built storage memory
- Dual modes for varied calculations
- Worksheet mode for advanced calculations
- Slide-on protective cover
- Bestselling financial calculator on Amazon

**Picking The Best Calculator For Statistics**

Thanks to different schools recommending different statistical calculator models that they are familiar with, it has become a lot more difficult to select one. But in many cases, it may be in your best interests to select the model that your teacher recommends. That’s because they will be using it extensively during graphing and even though a different model may work just as well, you’d be a lot more comfortable comparing what’s being taught in class with the same one.

Other than that, here are some of the features that you’d want to look out for while selecting the best calculator for statistics.

**Size**

Statistic calculators have largely remained unchanged over the years. And for that reason most people do not attribute too much to the size. But if you are going to be carrying the calculator for exams and tests, then it is better if you pick one that’s easier to lug. A standard size for these units is between 6-9 inches. Anything bigger is best worth a miss. There are smaller units too but the usability is questionable at best.

**Usability**

Considering that you will be spending a lot of time clacking away on the keys, look for a calculator that has an evenly spaced keypad. The keys should be easy to press but they should have a responsive feel to the touch. Anything that is overly small will have keys cramped really close together and that’s a recipe for disaster while performing precise calculations.

**Display**

The most desirable ones have a full multi colored LCD display. But even black and white displays work equally well provided that the numbers are sharp and crisp. You will be using the calculator in differently lit rooms. So, the display is of penultimate importance.

**Features**

Apart from the type of calculations that you can perform, there are many other features that can make life simpler while you are using the best statistical calculator. The playback feature or a rewind feature as it is called in some models, allows you to go back and alter a formula or a calculation. Advanced graphing will be immensely helpful in both statistical as well as scientific calculations.

### Statistical Calculations Meaning

An internal storage memory allows you to store your calculations for future reference. USB connectivity will let you transfer the data from the calculator to a computer and vice a versa. Some advanced calculator models even support Wi-Fi these days allowing you to wirelessly transmit data. When it comes to features, the sky is the limit. But an often overlooked one is a sliding protective cover that keeps the keypad safe from wear and tear due to repeated use.

**Price**

It goes without saying that you wouldn’t want to spend a huge amount to get a decent statistical calculator. And to that end, we have picked some amazing budget priced models for you. But as they say, you get what you pay for. The tradeoff is that lower priced models will rarely be as feature rich as the regular priced ones.

That’s it folks. We hope that this helps you select the right statistical calculator for use in your exams and class. If you have your own favorite model that you would like us to add to this list, please share it with us in the comments section.