BSC STATISTICS BOOK

Best Reference Books – bestthing.info – Statistics We have compiled a list of best reference books in Statistics for students doing bestthing.info in this. bestthing.info (HONOURS) STATISTICS SCHEME OF EXAMINATION Examination and 10 marks will be allocated to the record book and 5 marks to the oral test. We have compiled a list of best reference books in Statistics for students doing B. Sc. in this area. These books are used by Statistics students of.

This post on best statistics books is to give you a heads up on statistical know- how & a sneak peek in what those books propose and their best takeaways. Class Bsc Book Statistics All Chpter Wise Notes - Free download as Word Doc . doc /.docx), PDF File .pdf), Text File .txt) or read online for free. Class Bsc. Find free statistics and mathematics books in this category. Are you looking for a specific subject? Try one of the subcategories, for example: Calculus, Algebra.

You will learn to write reports based on these topics which will help you in further studies. This prospectus may be updated over the duration of the course, as modules may change due to developments in the curriculum or in the research interests of staff.

Year two Combining three compulsory modules with your choice from a range of optional modules, you will continue to study statistics, probability and applied mathematics in more depth and have the option to choose some modules from outside mathematics. Core modules Introduction to Scientific Computation This module introduces basic techniques in numerical methods and numerical analysis which can be used to generate approximate solutions to problems that may not be amenable to analysis.

Fundamental concepts relating to probability will be discussed in detail, including well-known limit theorems and the multivariate normal distribution. You will then progress onto complex topics such as transition matrices, one-dimensional random walks and absorption probabilities. Statistical Models and Methods The first part of this module provides an introduction to statistical concepts and methods and the second part introduces a wide range of techniques used in a variety of quantitative subjects.

The key concepts of inference including estimation and hypothesis testing will be described as well as practical data analysis and assessment of model adequacy. Optional modules Complex Functions In this module you will learn about the theory and applications of functions of a complex variable using a method and applications approach. You will develop an understanding of the theory of complex functions and evaluate certain real integrals using your new skills.

Differential Equations and Fourier Analysis This course is an introduction to Fourier series and integral transforms and to methods of solving some standard ordinary and partial differential equations which occur in applied mathematics and mathematical physics. The course describes the solution of ordinary differential equations using series and introduces Fourier series and Fourier and Laplace transforms, with applications to differential equations and signal analysis.

Standard examples of partial differential equations are introduced and solution using separation of variables is discussed. Mathematical Analysis In this module you will build on the foundation of knowledge gained from your core year one modules in Analytical and Computational Foundations and Calculus. You will learn to follow a rigorous approach needed to produce concrete proof of your workings.

Furthermore, it aims to introduce students to the fundamental mathematical concepts required to model the flow of liquids and gases and to apply the resulting theory to model physical situations. Professional Skills for Mathematicians This module will equip you with valuable skills needed for graduate employment.

You will work on two group projects based on open-ended mathematical topics agreed by your group. You will also work independently to improve your communication skills and learn how to summarise technical mathematical data for a general audience.

You will be provided with some commercial and business awareness and explore how to use your mathematical sciences degree for your future career. The laws of classical mechanics are investigated both in their original formulation due to Newton and in the mathematically equivalent but more powerful formulations due to Lagrange and Hamilton. Applications are made to problems such as planetary motion, rigid body motion and vibrating systems.

Quantum mechanics is developed in terms of a wave function obeying Schroedinger's equation, and the appropriate mathematical notions of Hermitian operators and probability densities are introduced. Applications include problems such as the harmonic oscillator and a particle in a three-dimensional central force field. Year three You will choose from a wide range of advanced optional modules which focus mainly on statistics, probability and their applications.

Depending on what you're trying to accomplish, it may not be necessary to find the boundaries. Tally the data. Find the frequencies. Find the cumulative frequencies.

Depending on what you're trying to accomplish, it may not be necessary to find the cumulative frequencies. It is possible to have the TI calculator find the frequencies for you. You will have to find the class width and class boundaries first.

Lists and Statistics There are two features of the TI calculator that will be used. Lists and Statistics. There are six lists that you can work with at any time on the calculator.

Each set of data requires a list. The lists are labeled L1, L2, L3, L4, L5, and L6 and are accessed on the calculator by pressing "2nd 1", "2nd 2", etc. Edit - Use this to enter data into a list. SortA - This will sort a list in ascending order. This is useful if you want to find the frequencies after you have already established the limits or boundaries. Since the data is sorted in order, you just have to go through and count the number in each class. You don't need to do the tally. This will replace the list you tell it sort.

SortD - This will sort a list in descending order.

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This will replace the list you tell it to sort. ClrList - This will erase any existing lists. It will handle both raw data and frequency distributions. This won't happen until the end of the semester. Setup - You will need to check the setup before you find any other statistical values from this menu. It allows you to specify which list s you put the data into and if necessary, which list contains the frequencies.

Med-Med - A regression model that isn't used in this course. QuadReg - A regression model that isn't used in this course.

CubicReg - A regression model that isn't used in this course. QuartReg - A regression model that isn't used in this course. The book uses this model, however, we will use 5 instead.

LnReg - A regression model that isn't used in this course. ExpReg - A regression model that isn't used in this course. PwrReg - A regression model that isn't used in this course. The dimension of a list the number of elements in the list. This is also used as a command to set the dimensions of a list. Fill - This command will fill a list with a constant.

This is useful if you need to set an entire list to all be one number. A list is returned, but you must save it to one of the six lists if you want to use it for anything. The mean is the sum of the list divided by the dimension of the list. The median is the middle number when the list is sorted in ascending order.

If the dimension is an even number, the median is the midpoint between the two middle values when the list is sorted in ascending order. If the product of a list is zero, then at least one of the numbers is zero. There are other values under statistics which you will use. You may have to arrow to other submenus first for some of them. This key will save values. You may save a scalar value to a real variable A-Z or a list value to a list L1 - L6. Lists can be used as arguments of functions.

If they are, the function is applied to each element in the list. Mathematical operations can be performed on lists. For more information on lists, see the Introduction to the TI Entering Data Always start with a clean set of data.

You don't want to mix data from one problem with data from another problem. Before starting any new problem, you should clear out existing data.

You may only need to specify one list, but you can specify more than one, just separate them with commas. Select this list that you want to use. The default will be L1. This will be fine for most things, but do realize you can use any of the lists. Just be sure to check the setup later. Type in each number separating them by enter.

Histograms, BoxPlots You can use the calculator to draw histograms, box-plots, and compute the frequency of each class. See the instructions on using the calculator to do statistics and lists. This provides an overview as well as some helpful advice for working with statistics on the calculator.

Histograms 1. Enter the data. Determine the class width and the lower class boundary not limit of the first class using the techniques for creating grouped frequency distributions.

Turn off any regular plots: Hit enter while the cursor is on the equal sign to toggle between displaying the function equal sign highlighted and not displaying the function equal sign not highlighted. Select a plot usually plot 1 and hit enter 6. Turn the plot on by highlighting the ON and pressing enter. Set the TYPE to histograph last type 8.

Set the FREQ to 1. Put the lower class boundary for the first class in XMIN The XMAX value should be the lower class boundary for the first class plus the number of classes times the class width. YMIN should be set to 0 YMAX should be at least the largest frequency in any class. This is difficult to know if you're generating the histogram without first writing the table by hand.

If the histogram displayed doesn't fit on the screen, go back and change this number. A good initial guess might be the sample size divided by the number or classes. You might round up it to a nice number multiple of 5 or add one or two so that graph is completely shown on the screen.

If your YMAX is small say under 10 , you might want to set it to 1. This will determine how many marks are placed along the vertical axis.

Finding the Frequency 1. Generate a histogram first 2. The "min" value is the lower class boundary 4. The "max" value is the upper class boundary 5. The "n" value is the frequency for that class.

Use the left and right arrow keys to get the values for all the classes. Box Plots 1. Select a plot usually plot 1 and hit enter 5. Set the TYPE to box-plot 3rd type 7. You may use the left and right arrow keys to find all five numbers. Note that the calculator uses the quartiles instead of the hinges. The hinges and quartiles are the same unless the remainder when the sample size is divided by four is three. Plotting an Ogive The Ogive is a frequency polygon line plot graph of the cumulative frequency or the relative cumulative frequency.

The horizontal axis is marked with the class boundaries and the vertical axis is the frequency. All class boundaries are used -- there will be one more class boundary than the number of classes.

The following example assumes the class boundaries are in List 1 and the cumulative frequencies are in List 2.

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You are free to use any two lists that you desire, but you should make the appropriate adjustments in the instructions if you don't use List 1 and List 2.

Enter the class boundaries into List 1. Start with the lower boundary of the first class and end with the upper boundary of the last class. Enter the cumulative frequencies into List 2. Start with 0 for the first value because there is nothing less than the first lower class boundary. The XMAX value should be the upper class boundary of the last class YMAX should be set to the total frequency if using cumulative frequencies in List 2 and set to 1. There is no need to re-enter the data if you wish to use relative cumulative frequencies instead of cumulative frequencies.

Replace the by the total frequency. You can't put " " into the calculator. To replace relative cumulative frequencies with cumulative frequencies, change the division to multiplication. Place the frequencies or relative frequencies in List 1.

If the List 1 is empty or the sum of list 1 is zero, then you are instructed to put the frequencies in list 1. Turn off any graphs that may be on before running the PIE program. Otherwise, the graphs will overlay the pie chart and it will take longer to draw.

The program will ask the user if they wish to place the labels on the graph. If the user enters 1 for yes, then the values in List 1 will be placed in the graph. This is where the difference between frequencies or relative frequencies appear. This program will force the calculator into radian mode and turn the axes off, zoom standard and then zoom square. It will then draw a circle and proceed to draw the lines which define the pie graph.

Statistic Characteristic or measure obtained from a sample Parameter Characteristic or measure obtained from a population Mean Sum of all the values divided by the number of values. This can either be a population mean denoted by mu or a sample mean denoted by x bar Median The midpoint of the data after being ranked sorted in ascending order.

There are as many numbers below the median as above the median. Mode The most frequent number Skewed Distribution The majority of the values lie together on one side with a very few values the tail to the other side. In a positively skewed distribution, the tail is to the right and the mean is larger than the median.

In a negatively skewed distribution, the tail is to the left and the mean is smaller than the median.

Symmetric Distribution The data values are evenly distributed on both sides of the mean. In a symmetric distribution, the mean is the median. Weighted Mean The mean when each value is multiplied by its weight and summed. This sum is divided by the total of the weights. Midrange The mean of the highest and lowest values. Max - Min Population Variance The average of the squares of the distances from the population mean.

It is the sum of the squares of the deviations from the mean divided by the population size. The units on the variance are the units of the population squared. Sample Variance Unbiased estimator of a population variance. Instead of dividing by the population size, the sum of the squares of the deviations from the sample mean is divided by one less than the sample size.

The population standard deviation is the square root of the population variance and the sample standard deviation is the square root of the sample variance. The sample standard deviation is not the unbiased estimator for the population standard deviation.

Coefficient of Variation Standard deviation divided by the mean, expressed as a percentage. We won't work with the Coefficient of Variation in this course. Chebyshev's Theorem The proportion of the values that fall within k standard deviations of the mean. Chebyshev's theorem can be applied to any distribution regardless of its shape. Empirical or Normal Rule Only valid when a distribution in bell-shaped normal. Standard Score or Z-Score The value obtained by subtracting the mean and dividing by the standard deviation.

When all values are transformed to their standard scores, the new mean for Z will be zero and the standard deviation will be one. Percentile The percent of the population which lies below that value. The data must be ranked to find percentiles. Quartile Either the 25th, 50th, or 75th percentiles. The 50th percentile is also called the median. Decile Either the 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, or 90th percentiles.

Lower Hinge The median of the lower half of the numbers up to and including the median. The lower hinge is the first Quartile unless the remainder when dividing the sample size by four is 3. Upper Hinge The median of the upper half of the numbers including the median. The upper hinge is the 3rd Quartile unless the remainder when dividing the sample size by four is 3. Box and Whiskers Plot Box Plot A graphical representation of the minimum value, lower hinge, median, upper hinge, and maximum.

Some textbooks, and the TI calculator, define the five values as the minimum, first Quartile, median, third Quartile, and maximum. Five Number Summary Minimum value, lower hinge, median, upper hinge, and maximum.

Outlier An extremely high or low value when compared to the rest of the values.

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Mild Outliers Values which lie between 1. Note, some texts use hinges instead of Quartiles. Extreme Outliers Values which lie more than 3. Table of Contents.

The term "Average" is vague Average could mean one of four things. The arithmetic mean, the median, midrange, or mode. For this reason, it is better to specify which average you're talking about. Median The data must be ranked sorted in ascending order first. The median is the number in the middle. To find the depth of the median, there are several formulas that could be used, the one that we will use is: The median is the number in the "depth of the median" position.

If the sample size is even, the depth of the median will be a decimal -- you need to find the midpoint between the numbers on either side of the depth of the median. Find the cumulative frequencies for the data. The first value with a cumulative frequency greater than depth of the median is the median. If the depth of the median is exactly 0. Since the data is grouped, you have lost all original information. Some textbooks have you simply take the midpoint of the class.

This is an over-simplification which isn't the true value but much easier to do. The correct process is to interpolate. Find out what proportion of the distance into the median class the median by dividing the sample size by 2, subtracting the cumulative frequency of the previous class, and then dividing all that bay the frequency of the median class.

Multiply this proportion by the class width and add it to the lower boundary of the median class. Mode The mode is the most frequent data value. There may be no mode if no one value appears more than any other. There may also be two modes bimodal , three modes trimodal , or more than three modes multi-modal.

For grouped frequency distributions, the modal class is the class with the largest frequency. Summary The Mean is used in computing other statistics such as the variance and does not exist for open ended grouped frequency distributions 1. It is often not appropriate for skewed distributions such as salary information. The Median is the center number and is good for skewed distributions because it is resistant to change. The Mode is used to describe the most typical case. The mode can be used with nominal data whereas the others can't.

The mode may or may not exist and there may be more than one value for the mode 2. The Midrange is not used very often. It is a very rough estimate of the average and is greatly affected by extreme values even more so than the mean. You can also find the measures of variation with the TI calculator. It is simply the highest value minus the lowest value.

Since the range only uses the largest and smallest values, it is greatly affected by extreme values, that is - it is not resistant to change. The range only involves the smallest and largest numbers, and it would be desirable to have a statistic which involved all of the data values.

The first attempt one might make at this is something they might call the average deviation from the mean and define it as:. The problem is that this summation is always zero. So, the average deviation will always be zero.

That is why the average deviation is never used. So, to keep it from being zero, the deviation from the mean is squared and called the "squared deviation from the mean". This "average squared deviation from the mean" is called the variance.

One would expect the sample variance to simply be the population variance with the population mean replaced by the sample mean. However, one of the major uses of statistics is to estimate the corresponding parameter.

To counteract this, the sum of the squares of the deviations is divided by one less than the sample size. Standard Deviation There is a problem with variances. Recall that the deviations were squared. That means that the units were also squared. To get the units back the same as the original data values, the square root must be taken. The calculator does not have a variance key on it. It does have a standard deviation key. You will have to square the standard deviation to find the variance.

Sum of Squares shortcuts The sum of the squares of the deviations from the means is given a shortcut notation and several alternative formulas. What's wrong with the first formula, you ask? Total the data values: Divide by the number of values to get the mean: Subtract the mean from each value to get the numbers in the second column. Square each number in the second column to get the values in the third column.

Total the numbers in the third column: Divide this total by one less than the sample size to get the variance: Not too bad, you think. But this can get pretty bad if the sample mean doesn't happen to be an "nice" rational number. Those subtractions get nasty, and when you square them, they're really bad. Another problem with the first formula is that it requires you to know the mean ahead of time.

For a calculator, this would mean that you have to save all of the numbers that were entered. The TI does this, but most scientific calculators don't. Now, let's consider the shortcut formula. The only things that you need to find are the sum of the values and the sum of the values squared.

There is no subtraction and no decimals or fractions until the end. The last row contains the sums of the columns, just like before. Record each number in the first column and the square of each number in the second column. Total the first column: Total the second column: Compute the sum of squares: Chebyshev's Theorem The proportion of the values that fall within k standard deviations of the mean will be.

Empirical Rule The empirical rule is only valid for bell-shaped normal distributions. The following statements are true.

The empirical rule will be revisited later in the chapter on normal probabilities. Using the TI to find these values You may use the TI to find the measures of central tendency and the measures of variation using the list handling capabilities of the calculator. Standard Scores z-scores The standard score is obtained by subtracting the mean and dividing the difference by the standard deviation.

The symbol is z, which is why it's also called a z-score. The mean of the standard scores is zero and the standard deviation is 1. This is the nice feature of the standard score -- no matter what the original scale was, when the data is converted to its standard score, the mean is zero and the standard deviation is 1. The data must be ranked. Rank the data 2. If this is an integer, add 0. If it isn't an integer round up. Find the number in this position. If your depth ends in 0. It is sometimes easier to count from the high end rather than counting from the low end.

If you wish to find the percentile for a number rather than locating the kth percentile , then. Take the number of values below the number 2. Add 0. Divide by the total number of values 4.

Convert it to a percent. The percentiles divide the data into equal regions. The deciles divide the data into 10 equal regions. The instructions are the same for finding a percentile, except instead of dividing by in step 2, divide by The quartiles divide the data into 4 equal regions. Instead of dividing by in step 2, divide by 4.

The 2nd quartile is the same as the median. The 1st quartile is the 25th percentile, the 3rd quartile is the 75th percentile. The quartiles are commonly used much more so than the percentiles or deciles. The TI calculator will find the quartiles for you.

Some textbooks include the quartiles in the five number summary. Hinges The lower hinge is the median of the lower half of the data up to and including the median. The upper hinge is the median of the upper half of the data up to and including the median.

The statement about the lower half or upper half including the median tends to be confusing to some students. If the median is split between two values which happens whenever the sample size is even , the median isn't included in either since the median isn't actually part of the data.

The median will be in position The lower half is positions 1 - 10 and the upper half is positions 11 - The lower hinge is the median of the lower half and would be in position 5. The upper hinge is the median of the upper half and would be in position 5. The median is in position The lower half is positions 1 - 11 and the upper half is positions 11 - The lower hinge is the median of the lower half and would be in position 6. The upper hinge is the median of the upper half and would be in position 6 when starting at position 11 -- this is original position Five Number Summary The five number summary consists of the minimum value, lower hinge, median, upper hinge, and maximum value.

Some textbooks use the quartiles instead of the hinges. Box and Whiskers Plot A graphical representation of the five number summary. A box is drawn between the lower and upper hinges with a line at the median. Whiskers a single line, not a box extend from the hinges to lines at the minimum and maximum values.

Interquartile Range IQR The interquartile range is the difference between the third and first quartiles. That's it: Q3 - Q1. There are mild outliers and extreme outliers. The Bluman text does not distinguish between mild outliers and extreme outliers and just treats either as an outlier.

Extreme outliers are any data values which lie more than 3. Mild outliers are any data values which lie between 1. Definitions Factorial A positive integer factorial is the product of each natural number up to and including the integer. Permutation An arrangement of objects in a specific order. Tree Diagram A graphical device used to list all possibilities of a sequence of events in a systematic way.

Every integer greater than one is either prime or can be expressed as an unique product of prime numbers. If there is a solution to a linear programming problem, then it will occur at a corner point or on a boundary between two or more corner points.

Fundamental Counting Principle In a sequence of events, the total possible number of ways all events can performed is the product of the possible number of ways each individual event can be performed. The Bluman text calls this multiplication principle 2. Factorials If n is a positive integer, then n!

Permutations A permutation is an arrangement of objects without repetition where order is important. A permutation of n objects, arranged into one group of size n, without repetition, and order being important is:. A permutation of n objects, arranged in groups of size r, without repetition, and order being important is:.

Sometimes letters are repeated and all of the permutations aren't distinguishable from each other. If you just write "B" as "B", however If a word has N letters, k of which are unique, and you let n n1, n2, n3, Here are the frequency of each letter: Combinations A combination is an arrangement of objects without repetition where order is not important. The difference between a permutation and a combination is not whether there is repetition or not -- there must not be repetition with either, and if there is repetition, you can not use the formulas for permutations or combinations.

The only difference in the definition of a permutation and a combination is whether order is important. A combination of n objects, arranged in groups of size r, without repetition, and order being important is:. They also form a pattern known as Pascal's Triangle.

Each element in the table is the sum of the two elements directly above it. Each element is also a combination. The n value is the number of the row start counting at zero and the r value is the element in the row start counting at zero.

Bsc Statistics Notes pdf - 1st, 2nd, 3rd and 4th Year Notes

Pascal's Triangle illustrates the symmetric nature of a combination. Since combinations are symmetric, if n-r is smaller than r, then switch the combination to its alternative form and then use the shortcut given above. TI You can use the TI graphing calculator to find factorials, permutations, and combinations. Tree Diagrams Tree diagrams are a graphical way of listing all the possible outcomes. The outcomes are listed in an orderly fashion, so listing all of the possible outcomes is easier than just trying to make sure that you have them all listed.

It is called a tree diagram because of the way it looks. The first event appears on the left, and then each sequential event is represented as branches off of the first event.

The tree diagram to the right would show the possible ways of flipping two coins. The final outcomes are obtained by following each branch to its conclusion: They are from top to bottom: Definitions Probability Experiment Process which leads to well-defined results call outcomes Outcome The result of a single trial of a probability experiment Sample Space Set of all possible outcomes of a probability experiment Event One or more outcomes of a probability experiment Classical Probability Uses the sample space to determine the numerical probability that an event will happen.

Also called theoretical probability. Equally Likely Events Events which have the same probability of occurring. Complement of an Event All the events in the sample space except the given events. Empirical Probability Uses a frequency distribution to determine the numerical probability. An empirical probability is a relative frequency. It employs opinions and inexact information. Mutually Exclusive Events Two events which cannot happen at the same time.

Disjoint Events Another name for mutually exclusive events. Independent Events Two events are independent if the occurrence of one does not affect the probability of the other occurring. Dependent Events Two events are dependent if the first event affects the outcome or occurrence of the second event in a way the probability is changed. Conditional Probability The probability of an event occurring given that another event has already occurred. Bayes' Theorem A formula which allows one to find the probability that an event occurred as the result of a particular previous event.

However, some sample spaces are better than others. Consider the experiment of flipping two coins. Thai qualifications Higher Secondary School Certificate Mathayom Suksa 6 Unfortunately we are unable to accept students onto our degrees on the basis of this qualification alone.

Emirati qualifications Secondary School Certificate Tawjihiyya Unfortunately we are unable to accept students onto our degrees on the basis of this qualification alone. Our entry requirements are listed under the 'United States of America' section.

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Russian qualifications Certificate of Secondary Education Attestat o Polnom Srednem Obshchem Obrazovanii Unfortunately we are unable to accept students onto our degrees on the basis of this qualification alone. Japanese qualifications Upper Secondary School Leaving Certificate Kotogakko Sotsugyo Shomeisho Unfortunately we are unable to accept students onto our degrees on the basis of this qualification alone.

We do not accept General Studies as one of these three subjects. We do not accept grade A- in place of grade A. South Korean qualifications Ilbankye Kodung Hakkyo General High School Diploma Unfortunately we are unable to accept students onto our degrees on the basis of this qualification alone.

Polish qualifications Certificate of Maturity 90, 85, 85 in three extended subjects including 90 in Mathematics plus grade 2 in any STEP.All hypothesis testing is done under the assumption the null hypothesis is true! This could be A levels, the International Baccalaureate Diploma or a recognised foundation course. It is possible to get 0 heads, 1 head, or 2 heads.

Data is classified according to the highest level which it fits. To get the units back the same as the original data values, the square root must be taken.

Mean, Variance, and Standard Deviation The mean, variance, and standard deviation of a binomial distribution are extremely easy to find.

Total the numbers in the third column: Turn off any graphs that may be on before running the PIE program.

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