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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsStatistics and ProbabilityBasics of Probability

### Statistics to Predict Future

Learn how data collected can be used to predict future. This is an important lesson, and it is not found in any other books or websites.

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Consider the number of glasses of water students drink during normal day and sunny day. Today is a hot sunny-day. Can one predict how many students would require 4 glasses of water?

One student says : As per the data in the table, we can expect more or less 9 students will drink 4 glasses of water.

Another student says : The data represents the number of students who had 4 glasses of water yesterday. There is no way we can predict how many will take today.

Is it possible to predict the future with data?

• Yes. We can expect more or less to the value in the data.
• Yes. We can expect more or less to the value in the data.
• No. It will never be possible to predict

The answer is "Yes. We can expect more or less to the value in the data".

Consider the number of glasses of water students drink during normal day. The data is collected for 40 students. Next day another class of 40 students is considered. Can one predict the data for another class of 40 students?

• Yes. The data would be more or less same.
• Yes. The data would be more or less same.
• No. The data would be completely different.

The answer is "Yes. The data would be more or less same". The data may not be exactly equal, but one can expect that the data would be more or less same.

Consider the number of glasses of water students drink during normal day. The data is collected for 40 students. Next day another class of 80 students is considered. Can one predict the data for the class of 80 students?

• Yes. The data would be more-or-less double of the data for 40 students.
• Yes. The data would be more-or-less double of the data for 40 students.
• No. The data would be completely different.

The answer is "Yes. The data would be more-or-less double of the data for 40 students". The data may not be exactly double, but one can expect that the data would be more or less double.

Consider the number of glasses of water students drink during normal day. The data is collected for 40 students. Next day another class of 20 students is considered. Can one predict the data for the class of 20 students?

• Yes. The data would be more-or-less half of the data for 40 students.
• Yes. The data would be more-or-less half of the data for 40 students.
• No. The data would be completely different.

The answer is "Yes. The data would be more-or-less half of the data for 40 students". The data may not be exactly half, but one can expect that the data would be more or less half.

Consider the number of glasses of water students drink during normal day. The data is collected for 40 students at the end of the day. Students are lined-up and one by one students provide information how many glasses of water they drank.  •  First student says, 2 glasses

•  Second student says, 3 glasses

•  Third student says, 1 glass

And so on, Which of the following describe the data of each student?

• 11 students out of 40 would say 1 glass
• 18 students out of 40 would say 2 glasses
• 6, 2, and 3 out of 40 would say 3, 4, and 5 glasses respectively.
• all the above
• all the above

The answer is "All the above". Note that the table is interpreted for one person at a time.

Consider the number of glasses of water students drink during normal day. The data is collected for 40 students. One day, only 1 student is considered. Can one predict how many glasses the student would drink?

• Yes. One can predict the data for one student.
• No. Any prediction is not possible at all for one student.
• Yes and No, the prediction for one student can be given only in the context of large data.
• Yes and No, the prediction for one student can be given only in the context of large data.

The answer is "Yes and No, the prediction for one student can be given, but only in the context of large data.".

Consider the number of glasses of water students drink during normal day. The data is collected for 40 students. Next day, only 1 student is considered. It is clear that, with certainty, it is not possible to predict the number of glasses the student will report. The possible prediction based on the recorded-data is given below.

If the data-collection is repeated 40 times,

•  the data-value 1 glass would appear 11 times out of the 40 times

•  the data-value 2 glasses would appear 18 times out of the 40 times

•  the data-value 3 glasses would appear 6 times out of the 40 times

•  the data-value 4 glasses would appear 2 times out of the 40 times

•  the data-value 5 glasses would appear 3 times out of the 40 times.

This is referred as : "probability" of the data value 1 is 11//40.

Let us consider another form of data. A person is tossing a coin, and recording the data. The data is shown in in the tally and tabular form for 40 tosses. If the coin is tossed 10 times, can one predict the result?

• Yes, the coin will have more or less 5 times heads and 5 times tail
• Yes, the coin will have more or less 5 times heads and 5 times tail
• No, it is not possible to predict.

The answer is "Yes, the coin will have more or less 5 times heads and 5 times tails".

Considering data from tossing a coin. If the coin is tossed once, can one predict the result?

• Yes, the best one can say is the result will be come as heads for 20 times in 40 repetitions
• Yes, the best one can say is the result will be come as heads for 20 times in 40 repetitions
• No, it is not possible to predict.

The answer is "Yes, the best one can say is the result will be come as heads for 20 times in 40 repetitions".

Predicting Based on Representative Data: Data can be used to predict the outcome of events.

Data is collected over a large number of iterations/repetitions.

It is known the result of one iteration can be one of many possibilities.

The result of one iteration is predicted in the context of the large-number-of-repetitions.

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