Basic Statistics And Probability By Shahid Jamal Pdf 49

Basic Statistics and Probability by Shahid Jamal: A Review

Basic Statistics and Probability by Shahid Jamal is a textbook that covers the fundamental concepts and methods of statistics and probability for undergraduate students. The book aims to provide a clear and concise introduction to the topics, with examples, exercises, and solutions. The book is divided into two parts: Part I covers descriptive statistics, probability theory, random variables, and distributions, while Part II covers inferential statistics, sampling techniques, estimation, hypothesis testing, correlation, and regression.

The book is written in a simple and easy-to-understand language, with a focus on practical applications. The book also provides a brief overview of some advanced topics, such as Bayesian statistics, geometric distribution, and binomial probability distribution. The book is suitable for students of mathematics, engineering, economics, business, and social sciences who want to learn the basics of statistics and probability.

The book has been widely used by students and teachers in Pakistan and abroad. The book has received positive feedback from the readers, who appreciate its clarity, comprehensiveness, and relevance. The book is available in PDF format for download from various websites[^1^] [^2^] [^3^] [^4^]. The book has 49 chapters and 672 pages.

In this article, we will review some of the main topics and concepts covered in the book. We will also provide some examples and exercises to help the readers understand and practice the material.

Descriptive Statistics

Descriptive statistics are used to summarize and display the data in a meaningful way. The book covers the following topics in descriptive statistics:

Types of data: qualitative and quantitative, discrete and continuous, nominal, ordinal, interval, and ratio.

Measures of central tendency: mean, median, mode, and their properties and applications.

Measures of dispersion: range, interquartile range, variance, standard deviation, coefficient of variation, and their properties and applications.

Measures of skewness and kurtosis: how to measure the asymmetry and peakedness of a distribution.

Frequency distributions: how to organize and present data in tables and graphs.

Graphical methods: how to use histograms, frequency polygons, ogives, pie charts, bar charts, stem-and-leaf plots, box plots, and scatter plots to display data.

The book provides many examples and exercises on descriptive statistics, with solutions at the end of each chapter. For example:

Example 1.1: The following table shows the marks obtained by 30 students in a statistics test. Calculate the mean, median, mode, range, interquartile range, variance, standard deviation, coefficient of variation, skewness, and kurtosis of the marks.

MarksFrequency

10-192

20-294

30-396

40-498

50-595

60-693

70-792

Solution:

We can use the following formulas to calculate the required measures:

The mean is given by $$\\bar{x}=\\frac{\\sum f x}{\\sum f}$$ where $f$ is the frequency and $x$ is the midpoint of each class interval.

The median is the middle value of the data when arranged in ascending or descending order. If the number of observations is odd, the median is the middle observation. If the number of observations is even, the median is the average of the middle two observations.

The mode is the most frequently occurring value or class interval in the data.

The range is the difference between the maximum and minimum values in the data.

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). The quartiles are the values that divide the data into four equal parts. Q1 is the median of the lower half of the data. Q3 is the median of the upper half of the data.

The variance is given by $$s^2=\\frac{\\sum f(x-\\bar{x})^2}{\\sum f}$$ where $s^2$ is the sample variance and $\\bar{x}$ is the sample mean.

The standard deviation is given by $$s=\\sqrt{s^2}$$ where $s$ is the sample standard deviation and $s^2$ is the sample variance.

The coefficient of variation (CV) is given by $$CV=\\frac{s}{\\bar{x}}\\times 100\\%$$ where $CV$ is the coefficient of variation, $s$ is the sample standard deviation, and $\\bar{x}$ is the sample mean.

The skewness is given by $$\\gamma_1=\\frac{\\sum f(x-\\bar{x})^3}{\\sum f s^3}$$ where $\\gamma_1$ is the sample skewness coefficient, $x$ is the midpoint of each class interval, $\\bar{x}$ is

the sample mean, $f$ is the frequency, and $s$ is

the sample standard deviation. aa16f39245