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Statistics and Probability
For example one variable that you want to describe statistically is the Mathematics Grade Score of 14 students in 4th grade.
Here your one variable = Mathematics Grade Score of 4th graders.
Because the procedure and calculation are the same for any one variable that you want to describe statistically, mathematician often use to generalize the equation or formula for computing the mean, median, mode, and standard deviation, so they often use the one variable, x = to represent the variable that you want to describe using statistical analysis of minimum, maximum, mean, median, deviation, and quartile.
Boxplot is also called Box and Whisker plot. Why do you need to learn this? Because if you are using enterprise corporation software like Tableau software for data visualization, you will encounter Box and Whisker plot as one of the options. So as a student to become college and career ready, you need to acquire this knowledge. Important to remember
1. Always arrange your data point from lowest to highest, hence called ordered statistical analysis
2. Count the number of your data points or records or observation. The number of count is represented by letter variable "n". In Excel, using Rank and Percentile data analysis, you see the default column name "Point" = 7 ; Value = 2589 ; Rank = 1 ; Percent = 100% . It means Record number 7 from your original data list . If you are using SAS statistical analysis, this will be called "Observation" = 7. It means the same thing record number 7 when you count your original data list from top to bottom.
Now you can answer the question what is the value of the lower whisker? = 70 is the answer
3. minimum value is also called the lower whisker
Can you answer the question what is the value of maximum whisker? = 78 is the answer
4. maximum value is also called the maximum whisker
Now if you are ask,"Tell me what is the median or middle value of your ordered data point ?" You see the middle is between 73 and 75. So you are confused, which one? To solve that confusion, statistician created the rule to get a uniform answer. The rule is you add the two middle number and divide it by 2. Now everybody agreed the median value is 74.
Median is also called the second quartile meaning 2/4 simplifying the fraction becomes 1/2 which correspond to the middle or median of your ordered list.
5. First quartile (1/4) , represented by variable name, Q1 means from overall median (1/2) to the minimum , you find the middle (1/2) value. In fraction 1/2 * 1/2 = 1/4. The word quarter means 1/4. From your ordered list of student's grade, the first quartile (Q1) student has a grade of 71.
6. Third quartile (3/4), represented by variable name, Q3 means from overall median (1/2) to the maximum, you find the middle (1/2) value. Why it is called third quartile? because you are counting the equal sharing from the minimum up to the third quartile line. Mathematically you added the first quartile (1/4) + second quartile (1/4) + third quartile (1/4) = 3/4 . So what is the grade of the third quartile (Q3) student? = 76 answer
7. the rectangular box is also called the inter-quartile, the range between Q3-Q1. Mathematically 3/4 - 1/ 4 = 2/4 = 1/2 = 0.50 in decimal = 50% in percentage
Why is the box or inter-quartile important? Because some decision makers want to know the range of the 50% of the population of data being analyze, " Tell me what is the range of grade of 50% of the student population ? ". Just by looking at the box, decision maker can answer that question quickly, the range of student's grade representing 50% of the total population is from 71 to 76. The short cut is just read the first quartile (Q1) value and the third quartile (Q3) value from the box and whisker plot. You should know by now where is the Q1 and Q3 location from the graph.
Shown below is a normal quartile plot and Histogram Graph. These two graphs give the user the ability to answer quickly different question such as:
1. Can you tell me how many student received a third quartile (Q3) grade? = 2 answer.
2. Can you tell me how many student received a maximum grade of 78? = 3 answer
3. How many student get a median grade or second quartile? = 0 answer from Histogram.
If the data points are so big in millions. Like for example the number of U.S. students are in millions. It is very hard to use the manual traditional statistical tools and visualization to answer important question and gain insight to do intervention for improvement. But thanks to machine learning we have now the tools to do another way of analysis that deals with big data.
1. To open probability distribution calculator click the ABC icon. Then select probability calculator. Statistics calculator comes with probability calculator.
2. To view the probability calculator only. Select the three horizontal line icon, select view. Then uncheck algebra view, uncheck graphics view, and check the probability calculator.
INTERACTIVE PROBABILITY AND STATISTICS FROM GEOGEBRA
Desmos Statistical Calculator
Follow the steps below using GeoGebra
Please wait while GeoGebra is downloading the interactive program. Follow the instructions below to view the statistics function from Geogebra.
Step 1. Click the icon three horizontal line 
then select view tab
Step 2. From view tab click algebra, to turn off the algebra function
Step 3. From view tab click spreadsheet, to turn on the spreadsheet
Step 4. From view tab click graphics, to turn off the graphics
Step 5. From view tab click input bar, to turn off the input bar
Step 6. In the spreadsheet view enter all the grades
Step 7. Follow the four steps shown above
By Apolinario "Sam" Ortega, 14 January 2013, Created with GeoGebra
Probability Distribution Next Lesson
Desmos Probability Distribution
Normal Distribution Probability
t - Distribution Probability
Chi-Squared Distribution Probability or X2 Probability
Probability Density Function (PDF) Calculator
Cumulative Density Function (CDF) Calculator
Click the link to learn more about central tendency location, dispersion, shape, histogram, confidence interval for mean, box and whisker chart, stem and leaves plot, and cumulative sum. You should click the "more" button on right hand side to view more statistical data.
Using Matlab Curve Fitting Mathematical Tools To Do Prediction or Inference.
Inference or Prediction is done automatically by machine or computer. This is an example of expert system, supervised machine learning that is well understood and easy to explain. Curve fitting is sometimes called glorified machine learning
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Source: How People Learn II: Learners, Contexts, and Cultures
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How can IN-V-BAT-AI be used in classrooms ?
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Personal Augmented Intelligence (AI) Explanation
🧠 Augmented Intelligence vs Artificial Intelligence
Understanding the difference between collaboration and automation
🔍 Messaging Contrast
Augmented Intelligence is like a co-pilot: it amplifies your strengths, helps you recall, analyze, and decide — but it never flies solo.
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| Year | Top 10 countries | Pages visited |
| 2023 | 1. USA 2. Great Britain 3. Germany 4. Canada 5. Iran 6. Netherlands 7. India 8. China 9. Australia 10. Philippines | 127,256 Pages / 27,541 Visitors |
| 2024 | 1. USA 2. China 3. Canada 4. Poland 5. India 6. Philippines 7. Great Britain 8. Australia 9. Indonesia 10. Russia | 164,130 Pages / 40,724 Visitors |
| Daily Site Visitor Ranking 10/15/2025 | 1. USA 2. Canada 3. Brazil 4. Vietnam 5. India 6. Argentina 7. China 8. Japan 9. Morocco 10. Indonesia | Year to Date 171,480 Pages / 57,831 Visitors |
Data source: Advanced Web Statistics 7.8
Approximately between 2.3 and 2.5 million schools globally, according to the latest available data from government and education ministry reports.
➡️ USA ~ Public 98,500 ~ Private 30,000 ~ Total 128,500 ➡️ Canada ~ Public 15,500 ~ Private 2,000 ~ Total 17,500 ➡️ Brazil ~ Public 138,000 ~ Private 40,000 ~ Total 178,000 ➡️ Vietnam ~ Public 42,000 ~ Private 8,000 ~ Total 50,000 ➡️ China ~ Public 217,200 ~ Private 152,800 ~ Total 470,000 ➡️ India ~ Public 1,022,386 ~ Private 335,844 ~ Total 1,358,230 ➡️ Japan ~ Public 30,240 ~ Private included ~ Total 30,240 ➡️ Morocco ~ Public 20,600 ~ Private 6,300 ~ Total 26,900 ➡️ Indonesia ~ Public 390,718 ~ Private included ~ Total 390,718 ➡️ Philippines ~ Public 47,831 ~ Private 13,000 ~ Total 60,831 Great Britain ~ Public 29,202 ~ Private included ~ Total 29,202 ➡️ Australia ~ Public 9,653 ~ Private included ~ Total 9,653 ➡️ Russia ~ Public 39,070 ~ Private included ~ Total 39,070 ➡️ Germany ~ Public 31,039 ~ Private included ~ Total 31,039 ➡️ Poland ~ Public 36,291 ~ Private included ~ Total 36,291 ➡️ Iran ~ Public 80,000 ~ Private included ~ Total 80,000 ➡️ France ~ Public 58,100 ~ Private included ~ Total 58,100 ➡️ Mexico ~ Public 132,505 ~ Private included ~ Total 132,505