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Statistics Calculators

SUBEDI CALCnew window   |  DESMOS Calculatornew window   |   STATKEYnew window    |  LibreTEXT Calculatorsnew window  

 

Random Number Generators

Generate Random Numbers

Random Number Generatornew window

This calculator allows you to generate random numbers between a start and end value. Option to allow duplicates is available.


Calculator Screenshot

Random Number Generator Calculator Image

Generating Random Values


Generate a random value sampled uniformly from the interval [0,1).

random()

Generate a list of n random values sampled uniformly from the interval [0,1).

random(n)

Generate a list of n random values sampled uniformly from the interval [0,1), using seed.

random(n, seed)

Desmos Random Number Generation

 

Generating Random Numbersnew window

Generate a random number between 0 and 1.

Ti Calc Image

[MATH] > PROB
Select 1:rand and ENTER

Generate n random number between 0 and 1.

Generate n Random Numbers between 0 and 1

[MATH] > PROB
Select 1:rand followed by ( n ) and ENTER

Generate n random number between lower and upper values.

Generate a random number between lower and upper values.

[MATH] > PROB
Select 5:randInt and enter lower, upper, and the number of random values to generate. Select Paste and press ENTER. Press ENTER again.

NOTE: For older operating systems, enter as 
randInt(1, 100, 5)

Generating Random Numbers (MS EXCEL, GOOGLE SHEETS, etc.)


Generate a random number between 0 and 1.

=RAND()

Generate a random integer between two values, inclusive.

=RANDBETWEEN(low, high)

Excel Rand() and Randbetween()
Summary Statistics: Five Number Summary, Standard Deviation, etc.

Descriptive Statistics

One Variable Statisticsnew window

Calculate one variable summary statistics for raw data or data presented in a frequency table.

One Variable Statistics

Calculator Screenshot showing calculation for data frequency table. For raw data, only the first column will show.

Weighted Mean and Expected Value Calculatornew window
Calculate weighted means from supplied data. For expected value, ensure the probabilities sum to 1.

Weighted Mean Calculator

DESMOS: Summary Statistics

Enter your raw data values as a comma separated list inside square brackets. Give the list a name so that the list can be referenced later for calculations. Example: L= [25,36,45,25,-6,25,48]

Desmos General Statistical Functionsnew window


Finding a 5-Number Summary using Desmos

Finding a 5-Number Summary using Desmos
Summary Statistics

 

One Variable Statistics Calculatornew window


 Enter data values in the text entry box. Separate values with commas. See screenshot below:

LibreText Online Calculator - One Variable Statistics

Descriptive Statistics for One Quantitative Variablenew window


On the main StatKey page, click on One Quantitative Variable under Descriptive Statistics and Graphs.
Enter your data by clicking on EDIT DATA button. 

Statkey Edit Data Entry

Manually edit the values or paste a tab or comma seperated file into the box and click Ok.

If updating a data file, ensure there's only one column (or two if there is an identifier).

 


After entering your data, you will see something similar to the image below:

 Descriptive Statistics for One Quantitative Variable

One-Variable Statistics


Entering Data and 1-Variable Statistics (TI-84 & TI-83)
Boxplot and Five-Number Summary (TI-83 & TI-84)
Graphs: Boxplots, Dotplots, Histograms, Scatterplots

Descriptive Statistics

Descriptive Statistics and Graphs

In addition to the summary statistics, StatKey also can nicely graph supplied data. Enter your data. For help with data entry, see the Edit Data section of Statkey tab inside Summary Statistics.

Once data values are entered, the default graph is dislayed. Choose the options below for various graph types and summaries.


Statkey Histogram Example

Data Visualizations in Desmosnew window


Dotplot, boxplot, and histograms

Data Visualizations in Desmos

Boxplot and Five-Number Summary (TI-83 & TI-84)


Boxplot and Five-Number Summary (TI-83 & TI-84)
Probability Distribution Calculators

Normal and Student-t distributions

Probability Distributions (Z, t)new window


Calculate cdf and inverse for Normal and Student-t distributions. For entered values, the results displayed are from Desmos. Desmos input entries are also displayed to help you use Desmos Graphing Calculator directly if you wish.

Probability Distributions (Z, t)

CDF and InverseCDF


On the StatKey Home Pagenew window main page, select either Normal or t for Theoretical Distributions row.

For normal distribution, you can change the mean and the standard deviation values by clicking on [ Edit Parameters ] button.

For Student-t, enter degrees of freedom (df), which you can change later as needed by clicking on [ Edit Parameters ] button.

Select Left Tail, Right Tail, or Two Tail and enter either an area/proportion/probability or values (x or z). Results will automatically be shown.


Screenshot showing Normal distribution example with two tails.

Normal and Student-t Distributions

Normal Dist Tail Areas on TI-83 & TI-84 Plus

Normal Dist Tail Areas on TI-83 & TI-84 Plus

Inverse Normal Distribution Calculations for TI-83 & TI-84

Inverse Normal Distribution Calculations for TI-83 & TI-84
Linear Regression and Correlation

Compute r, r2, and the Linear Regression equation

LINEAR REGRESSION and CORRELATIONnew window

Make sure to view the Regression Tournew window first before using Desmos for regressions.


Screenshot of Desmos Regression Entry

Regressions on Demos Calculator 

For linear regression, follow the Two Quantitative Variablesnew window link under Descriptive Statistics and Graphs on the main StatKey page. This is the same one from Descriptive statistics above.

Enter your data values by clicking on the EDIT Data button. Your summary statistics should automatically show. 

Use the options to switch variables or Show Regression Line as necessary.


Screenshot of Descriptive Statistics for Two Quantitative Variables with regression equation shown.

Descriptive Statistics for Two Quantitative Variables

Linear Regression on a TI-83 and TI-84

Linear Regression on a TI-83 and TI-84
Confidence Interval for Proportions

One sample and Two samples

Confidence Interval for Proportionsnew window


Calculate confidence interval (CI) for proportion for both one or two sample cases. CI is given in ± notation. Margin of Error is also shown.

Confidence Interval for a Proportion

CONFIDENCE INTERVAL for proportions Calculatornew window


Enter sample size, n, the number of successes, x, and the confidence level, CL (in decimal).  Press calculte to reveal the lower and upper bounds of the confidence interval. ONE SAMPLE case only.

Screenshot of the calculator

CONFIDENCE INTERVAL for proportions Calculator

1-Proportion Confidence Interval (TI-83 & TI-84)

1-Proportion Confidence Interval (TI-83 & TI-84)

2-Proportion Confidence Interval (TI-83 & TI-84)

2-Proportion Confidence Interval (TI-83 & TI-84)
Confidence Intervals for Means

One sample and Two samples

Confidence Interval for Meansnew window


Calculate confidence interval (CI) for proportion for both one or two sample cases. Options to use either data or sample statistics.

CI is given in ± notation. Margin of Error is also shown.

Confidence Interval for Means

One-Sample t-Interval for TI-83 & TI-84


The following video shows the process for computing a t-interval. Steps for z-interval are similar.
One-Sample t-Interval for TI-83 & TI-84
Sample Size Calculation for Confidence Intervals

Sample size for a Proportion or a Mean

Sample Size Calculatornew window
Sample size determination for Mean and Proportion.
 
Sample Size Calculator
Inference for the Proportion

Hypothesis Testing for the Proportion using ONE or TWO Samples

Inference for the Proportionnew window


Hypothesis testing for the proportion using either data or sample statistics from one sample or two samples. Option to include confidence interval in the results.

Inference for the Proportion

1-Proportion Z-Test (Hypothesis Testing) (TI-83 & TI-84)

1-Proportion Z-Test (Hypothesis Testing) (TI-83 & TI-84)

2-Proportion Z-Test (Hypothesis Testing) (TI-83 & TI-84)

2-Proportion Z-Test (Hypothesis Testing) (TI-83 & TI-84)
Inference for the Mean

Hypothesis Testing for the Mean using ONE or TWO Samples

Inference for the Meannew window


Hypothesis testing for the mean using either data or sample statistics from one sample or two samples. Options to include dependent samples and confidence interval. 

Inference for the Mean

One-Sample t-Test for TI-83 & TI-84


One-Sample t-Test for TI-83 & TI-84

2-Sample t-Test (TI-83 & TI-84)


2-Sample t-Test (TI-83 & TI-84)

Hypothesis Testing for the Difference Between Two Dependent Means Using the TI-84 (T-Test)


Hypothesis Testing for the Difference Between Two Dependent Means Using the TI-84 (T-Test)
column 2
Chi-Square Tests

Goodness of Fit, Independence, and Homogeneity Tests

Chi-Square Testsnew window


Included options are Goodness of Fitness, Independence, and Homogeneitry tests.

Chi-Square Tests

Test for Homogeneitynew window


 Test for Homogeneity

Test for Independencenew window


 Test for Independence

Goodness of Fitnew window


Goodness of Fit

 

 

Goodness of Fit Test (Chi-Square Test) (TI-83 & TI-84)


Goodness of Fit Test (Chi-Square Test) (TI-83 & TI-84)

Chi-Square Test for Independence for TI-83 & TI-84


Chi-Square Test for Independence for TI-83 & TI-84
Bootstrap Confidence Intervals

Bootstrap confidence Intervals using StatKey

Bootstrap Confidence Interval for:  Confidence Interval for a Meannew window    |    Difference in Meansnew window


STEP 1: Enter the original sample data into StatKey by clicking on Edit Data.


Bootstrap Edit Data Entry

Manually edit the values or paste a tab or comma seperated file into the box and click Ok.

If updating a data file, ensure there's only one column (or two if there is an identifier).

Note: Data entry and confidence interval calculation process for a difference in means is similar.


STEP 2: Generate several thousand samples (say, 10,000 samples) by clicking on the Generate 1000 Samples button several times.

If you're calculating Bootstrap confidence intervals by plugging in the standard error, use the value of std. error shown on the Bootstrap dotplot.
For 
PERCENTILE Method, continue with the following steps.

STEP 3: Select TWO-TAIL for confidence intervals. 

STEP 4: Change the middle area/proportion to match your confidence level. 

After STEP 4, the lower and upper bounds of your confidence interval are shown below the horizontal axis on the main graph. See image below.

Bootstrap Confidence Interval for a Mean

Bootstrap Confidence Interval for:   Proportionnew window    |    Difference in Proportionsnew window


Note: Data entry and confidence interval calculation process for a difference in proportions is similar.

STEP 1: Enter the original sample data into StatKey by clicking on Edit Data. Enter the sample size and the count/frequency for each sample in the dialog box.

STEP 2: Generate several thousand samples (say, 10,000 samples) by clicking on the Generate 1000 Samples button several times.

If you're calculating Bootstrap confidence intervals by plugging in the standard error, use the value of std. error shown on the Bootstrap dotplot. 
For PERCENTILE Method, continue with the following steps.

STEP 3: Select TWO-TAIL for confidence intervals. 

STEP 4: Change the middle area/proportion to match your confidence level. 

After STEP 4, the lower and upper bounds of your confidence interval are shown below the horizontal axis on the main graph. See image below.

Bootstrap Confidence Interval for a Proportion

Randomization Tests

Randomization Tests using Statkey

Randomization Test for a Meannew window    |    Randomization Test for a Difference in Meansnew window

Make sure to enter data first by clicking on EDIT Data. Enter sample data. Note that you will need raw sample data (not sample statistics) for randomization tests so that resampling can be performed for the test.

STEP 1: Enter your Null hypothesis value. For two sample cases, the Null will be already listed as µ1 = µ2.

STEP 2: Generate several thousand samples (say, 10,000 samples) by clicking on the Generate 1000 Samples button several times.

STEP 3: Select the tail type of your test. 

STEP 4: Change the value in the box below the horizontal axis to match your sample mean. For two sample tests, match the value below the axis with the difference in the means,  x̅1 − x̅2, displayed in the Original Sample section (top-right).

NOTE: For two-tailed tests, there will be two values under the horizontal axis. Change the value of the box that is of the same sign as the original sample statistic

STEP 5: For one-tailed test, this area is the p-value. For two-tailed tests, the p-value equals the total of the two tail areas. Area(s) representing p-value(s) will be shaded in red.


Randomization Test for Mean

Randomization Test for a Proportionnew window    |    Randomization Test for a Difference in Proportionsnew window


Make sure to enter sample information by first by clicking on EDIT Data. Enter your sample success(es) and sample size(s).

STEP 1: Enter your Null hypothesis value. For two sample cases, the Null will be already listed as p1 = p2.

STEP 2: Generate several thousand samples (say, 10,000 samples) by clicking on the Generate 1000 Samples button several times.

STEP 3: Select the tail type of your test. 

STEP 4: Change the value in the box below the horizontal axis to match your sample proportion (p-hat). For two sample tests, match the value below the axis with the difference in the sample proportions displayed at the bottom right of the table in the Original Sample section (top-right).

NOTE: For two-tailed tests, there will be two values under the horizontal axis. Change the value of the box that is of the same sign as the original sample statistic. 

STEP 5: For one-tailed test, this area is the p-value. For two-tailed tests, the p-value equals the total of the two tail areas. Area(s) representing p-value(s) will be shaded in red.


 Randomization Test for Proportion