# Smart Syllabus Statistics Class 12th | Intermediate Smart Syllabus FBISE

Smart Syllabus Statistics Class 12th | Intermediate Smart Syllabus FBISE.

## Smart Syllabus Statistics Class 12th:

1. Probability (1/8)
 Content Scope Brief revision of set theory, random experiment, sample space, events. Axiomatic and relative definition of probability. Conditional probability, multiplication theorem, (without proof) independence, application of addition theorem, counting rules, permutations and combinations and their real- world problems involving the computation of probabilities. In explaining ‘basic concepts’, givehe difference between certainty and  uncertainty by examples. Examples shall be selected from areas such as, business. Medicine, Agriculture, Astronomy, Psychology, etc. Also the applications of probability for prediction and forecasting be highlighted. Addition theorem of two events conditional probability, multiplication theorem be explained with the help of bivariate tables. Concept of independence be explained using classical logic through coins and dice as well as real events. In counting problems many examples be given for the calculation of number of combinations and permutations. The multiplication method of counting be explained through examples. While explaining applications of probability from real world problems, exercise be selected from different scientific fields such as Medicine, Meteorology, Engineering Agriculture, Space Sciences etc.

1. Discrete and continuous probability distribution (2/8)

 Content Scope Concept of random variable, discrete univariate probability distributions, joint and marginal probability, expectation and variance of discrete random variables, discrete uniform distributions generation and application of random numbers, continuous univariate probability distributions through geometrical concepts. Explain random variable by sample space, variable and probability. Explain the difference between mathematical variable and random variable: random variables can be discrete or continuous. Examples of random variables like number of patients in a clinic per day, number of accidents on a given road per weak, number of plants without followers per square yard in a given fields etc, be explained as real world examples of random variable. In discussing discrete variate: “Probability distribution expectation and variance”, use frequency tables for head and tails in coins, number of defective items in lots of five items
 etc, number of accidents per week on a certain road. Discrete uniform distribution to be discussed through random numbers which should be generated or obtained from random number tables. Discrete uniform distribution would thus be obtained and mean variance would be obtained from there. While doing this random number table on one page or more than one pages may be used. “Continuous univariate probability distributions”, would be those which can be sketched through linear functions such as F(x) = x + a from the lower limit  would be shown equating to one, and areas on smaller intervals would be shown as values of probability

1. Hypergeometric and Binominal Probability, Distributions (1/8)

 Contents Scope Bernoulli trails, Binominal distribution, its mean, variance, skewness and applications. Hypergeometric experiments to be explained through examples such as selecting a number of fish of particular type from a large pond, selecting a set of defective items from a production belt in a factory etc. Hypergeometric distribution to be explained using “M” balls in a box out of which “k” balls are white and (M-k) balls are black and “n” balls are drawn from the box, the probability expression would be explained. Special cases for specific values of “N”, “k” and “n” to be obtained. The expression for the mean and the variance of hyper geometric distribution to be given without derivation but to be explained thoroughly, “Bernoulli trails to be explained using black and white balls in a box, head and tail in case of a coin, boy and girl in a family, defective and nondefective items in a given large lot, sick and healthy people in a town etc. The evens would be defined in terms of the result of a given number of trails such as (HTTHH) occurring in a five trails from five losses of coin. The number of heads, the number of balls of a particular colour in a selection of (say ) 10 balls, etc be defined as the Binominal variable. The Binominal probability distribution to be explained by  first
 explaining Bernoulli trails, the mean and variance be derived. In the exercises, problems must be selected from fields such as Medicine, Agriculture, Engineering, Geology, Pharmacy and Psychology etc.

1. Normal Distribution (1/8)

 Content Scope Normal probability distribution and its properties, computation of probabilities (areas under the National Curve), applications in real life, kurtosis. Normal Probability distribution to be explained by writing the mathematical function with its parameters. The sketches of the normal distribution to be explained by : i.          Keeping parameter of mean as fixed and changing the standard deviation. ii.        Keeping the parameter of standard deviation as fixed and changing the parameter of mean. The standard normal distribution be explained and the tables of areas under the standard normal distribution be explained. Exercise be given so that for given intervals areas are obtained with the use of normal tables and also intervals are obtained when probabilities are given. Exercise based on fields such as, Medicine, business, agriculture, Psychology, Economics etc., be solved in sufficient number.
1. Sampling and sampling distribution (1/8)

 Content Scope Population and sample: advantages of sampling; sampling error and non-sampling error; probability and non-probability sampling sample random and stratified random sampling. Population and sample, advantages of sampling” be explained by stating that populations are usually large and not generally possible to observe each and every member of it. This problem be explained as kind of difficult situation to be solved. The importance of random sample be explained, which gives accurate results for the parameters of the population and is a useful statistical procedure to arrive at almost accurate results sampling be also explained as a useful technique for prediction. “Sampling error”, be explained as the amount of error that would occur while drawing the sample,. The measurement of sampling error
 be explained as a useful way of knowing the precision of the index, which is derived from the sample. “Non sampling error” be explained as those errors which cannot be eliminated. These occur in cases when there is a fault in the measuring scale or the observation kit. Examples of sampling be given from fields such as Agriculture, Medicine, Psychology, Economics etc. Selection of all possible samples from finite population with and without re-placement, parameter and statistic, sampling distributions of mean and proportion, concept of Central Limit Theorem. Explain the sampling distribution of the mean by first showing that sample mean is a random variable. In order to do this, selection of all possible samples from finite populations with and without replacement be explained. Explain the terms parameter and statistic as quantities related with the population and sample respectively. The sampling distribution of the variance be explained through examples based on a small set of observations. In the same way, the sampling distribution of proportion be explained also. Central limit theorem be explained to show the shape location and dispersion of the distribution of the sample mean when samples are large and when the distribution of the population is unknown or known to be non- normal.

1. Statistical inference (1/8)

 Content Scope Concept of statistical Inference: Point estimation of the population mean, variance and proportion: unbasedness of mean and proportion intervals for the mean of a normal population (known and unknown standard deviation), confidence interval of proportion (large samples).   Formulation of Alull and alternative hypotheses: type-I and type-II error, test of hypotheses for the mean of a normal population (known and unknown standard deviation). Explained standard inference by showing that the mean and variance parameters in a population are mostly unknown. Explain that mostly, samples are only available. Discuss the techniques of inference as a set of statistical procedures by which unknown parameters of the given population are estimated. Parameters be explained as point estimators, confidence interval, hypothesis to be tested. Explain point estimation of the population mean, variance and proportion by considering a finite population of four of  five observations and  by writing all the samples of two or three or four observations. Mean  and  variance be explained
 For population mean and proportion (large samples) with reference to such finite of mean and proportion explained with such finite populations as well. Explain the confidence Interval for the mean of a normal distribution when standard deviation is known by writing the probability express for standard normal variable on an interval and then converting it into a confidence interval and of “Mean”, When standard deviation is unknown, use of distribution and variable be explained. For population mean and proportion when the distribution is not given, large samples be considered so that central limit theorem could be applied. Explain the confidence Interval for the difference between means and proportions by considering large independent samples, s that central limit theorem is applicable. Explain Null hypothesis in its different forms i.e., simple and composite one sided and two sided. Explain the Test by considering sample mean and sample proportion. Type-I error and its probability X and Type-II error with its probability B be explained by using sketches of Normal Probability Curve. Calculation of X and B is not required. Test of hypothesis for the mean of the Normal Population be discussed by writing the steps (usually 8 or 9). Use of sketches be encouraged.

1. Association (1/8)

 Contents Scope Concept of categorical or qualitative data Bivariate categorical (qualitative) data; association versus independence of two qualitative variables; (Nominal and ordinals scales), contingency table; chi-square test of independence. Measurement of association between two qualitative variables through the method of rank correlation co-efficient. Explain the categorical data by considering categories in a unvariate case and in a bivariate case. It may further be explained using nominal and ordinal scales. It be explained that the most important statistical analysis in this type of data is known as association or independence. Real life examples be considered to explain various types of data. Explain the calculation of expected frequencies in a univariate and bivariate contingency table. Calculation of chi square to be explained by considering examples of un-variate and bivariate tables. Explain with examples the situation, where
 observations are ranked or ordered. Examples where two judges rank a group of competitors in a flower arrangement competition, the ranking of competitors in a fashion show or dish competition of food dishes or in competitions of paintings etc. The formula of rank correlation be given and applied in several examples.

## Previous News About Federal Board Intermediate Smart Syllabus:

At last came the news that all the students were eagerly waiting for. From the day the government announced to give smart syllabus from first class to tenth class, the students of class XI and XII have demanded that they should also be provided smart syllabus otherwise they will face many difficulties in preparing for next year’s exams.  Finally, today the Federal Board announced the awarding of 11th and 12th class class syllabus.

According to the notice, the federal board said that smart labs for 11th and 12th classes will be published next week. Now, as the Federal Board has announced to give smart syllabus, it is hoped that all other education boards will soon announce smart syllabus for class XI and XII.

### Smart Syllabus For Class 1 to 10:

It may be recalled that the syllabus of class I to X has already been published in schools and on the Internet and this syllabus has been started in schools.

### How much syllabus will be reduced for 11th and 12th Classes?

As the Federal Board has announced to give smart syllabus to 11th and 12th class students, it is hoped that other boards of education will also announce smart syllabus soon and this syllabus will be reduced by 3%.

### What is Smart Syllabus?

The Punjab Textbook Board announced the introduction of a new syllabus on August 5 called Smart Syllabus. This syllabus is fifty percent of the full year syllabus. According to some reports, it is also being said that this syllabus will be 60% of the syllabus of the whole year.

### For Which Classes Smart Syllabus will be available?

The Punjab Textbook Board has announced the introduction of a new syllabus for the annual examinations 2021 for first class to tenth class which has been named as Smart Syllabus. This syllabus was started in all public and private schools from September 2020 and will be completed by February 2021. The annual exams 2021 will also be taken on the basis of the same smart syllabus. This syllabus is 50% of the commonly given syllabus. This syllabus has also been made available on the internet after its publication and has been sent to all public and private schools.

### For Which Classes Smart Syllabus is available?

At present only ninth and tenth grade syllabus has been provided which has also been started in all public and private schools.

### Why Smart Syllabus is given to students?

It was unanimously decided by all the provinces that smart syllabuses should be given to the children so that next year’s annual examinations 2021 could be taken on time. The teachers also said that if the syllabus was not shortened, the children would be able to take the annual exams on time next year 2021.

### Smart Syllabus for 11th and 12th Class:

Eleventh and twelfth grade smart syllabus have not been introduced yet. It is also being heard that smart syllabuses of class XI and XII will not be given while students are also getting angry about how they will be able to give exams on time next year without smart syllabus so they should also be given smart syllabuses.

### From where you can get this smart syllabus?

As soon as the syllabus is published, we will inform you immediately on this website and also provide you the complete syllabus in detail.

### What is this website about?

This website Sound of the Soil Official deals with academic news, academic notices, exam results, exam date sheets, exam roll number slips, smart syllabuses for all parties, student scholarships, online admissions and guess papers for 9th, 10th,11th and 12th classes as well as trending and important news. It provides all the information about the all Educational Boards of Education across Pakistan including Federal Board,Bahawalpur Board,D.G.Khan Board,Faisalabad Board, Gujranwala Board, Lahore Board,Multan Board,Rawalpindi Board,Sargodha Board,Kohat Board, Abbottabad Board,Saidu Sharif Swat Board,Hyderabad Board,AJK Board,Balochistan Board,Sukkur Board.