Basic Statistics and Data Analysis

Statistics Lecture Notes, Online MCQs

Author: Muhammad Imdad Ullah

Miscellaneous Articles

 by 

Statistics Data Analysis Challenge – 1

The main objective of the “Statistics Data Analysis Challenge” is to learn how to analyze and interpret the data. All the submitted videos will be compiled into one video file and it will be shared with each participant and different social platforms. The video will also be uploaded on YouTube. All participants’ names and their relevant provided information will be marked on their videos.

This data set contains information on 78 people using one of three diets.  A short description of the variable is given below.

Variable nameVariableData type
PersonParticipant number 
genderGender, 1 = male, 0 = femaleBinary
AgeAge (years)Scale
HeightHeight (cm)Scale
preweightWeight before the diet (kg)Scale
DietDietCategorical
weight10weeksWeight after 10 weeks (kg)Scale
weightLOSTWeight lost after 10 weeks (kg)Scale

What to do with data:

  • You need to perform possible statistical analysis (data visualization, descriptive, and inferential) on this data using any statistical software.
  • You may check statistical assumptions for data and different inferential tests.
  • You may create new variable or recode the variables to perform different statistics.
  • You also need to shortly describe the results obtained.
  • You may record your own audio for explanation purpose or may insert text using and text editor.
  • For audio recording you may use your local language too, however preference is Urdu or English language.

What will you learn:

  1. You will learn the use of different statistical software with live demonstration of procedure
  2. You will learn how to perform the required statistical analysis on different type of data set or variables.
  3. You will learn how to interpret the results.
  4. You will learn what must be done before performing any statistical analysis
  5. You may also learn how to report or publish your results.

Challenge Requirements:

  1. You need to record the video of what ever you do with data. For example, import of data file, setting of variable properties, step by step procedure of performing any required statistical analysis (such as descriptive statistics, t-test, and possible graphs etc.)
  2. Each participant will submit only one file.
  3. For video recording you can use any screen recording software. You can use ‘Sharex’ or ‘apowersoft screen recorder software’ too.
  4. The total time of video must not exceed 10 minutes.
  5. File type should be mp4 with H.264/ H.265
  6. The resolution may be ‘640 x 480’, ‘1280 x 720’, and 1920 x 1080’
  7. You will email me (at [email protected]) the google drive or dropbox link of your ‘screen recorded video’ file.
  8. For help about Statistical Software you can visit: https://itfeature.com/statistical-softwares

Who Should Participate:
Any student, researcher, or teacher of Statistics

Download Data File:

Diet-DataDownload

Note: The pure objectivity of the “Statistics Data Analysis Challenge” is to promote the subject of Statistics in Pakistan.

Basic Statistics

 by 

MCQs Skewness & Kurtosis 11

This quiz contains MCQs Skewness and Kurtosis covering the shape of the distribution, Measures of central tendency such as mean, median, mode, Weighted mean, data and type of data, sources of data, Measures of Dispersion/ Variation, Standard Deviation, Variance, Range, etc. Let us start the MCQs Skewness Quiz.

1. The distribution is positively skewed if

 
 
 
 

2. The degree to which numerical data tend to spread out about an average value is called

 
 
 
 

3. The first three moments of a distribution about the mean $\overline{X}$ are 1, 4, and 0. The distribution is

 
 
 
 

4. If the moment Ratio $\beta_2=3$ then the distribution is

 
 
 
 

5. In Symmetrical distribution $Q_3-Q_1=20$, Median = 15, $Q_3$ is equal to

 
 
 
 

6. In symmetrical distribution if $Q_1=4, Q_3=12$ then median is

 
 
 
 

7. When a distribution is symmetrical and has one mode, the highest point on the curve is called the

 
 
 
 

8. For a symmetrical distribution

 
 
 
 

Basic statistics deals with the measure of central tendencies (such as mean, median, mode, weighted mean, geometric mean, and Harmonic mean) and measure of dispersion (such as range, standard deviation, and variances).

Basic statistical methods include planning and designing the study, collecting data, arranging, and numerical and graphically summarizing the collected data.

Basic statistics also used to perform statistical analysis to draw meaningful inferences.

MCQs Skewness

A basic visual inspection of data using some graphical and numerical statistics may give some useful hidden information already available in the data. The graphical representation includes a bar chart, pie chart, dot chart, box plot, etc.

Companies related to finance, communication, manufacturing, charity organizations, government institutes, simple to large businesses, etc. are all examples that have a massive interest in collecting data and measuring different sorts of statistical findings. This helps them to learn from the past, noticing the trends, and planning for the future.

There are various graphical and numerical ways that are used to check the skewness of the data. Skewness is the lack of symmetry in distribution.

Index Numbers

 by 

Index Number: An Introduction

Index Number

An index number is a number that “measures a relative change in a variable or an average relative change in a group of related variables with respect to a base”. An index number indicates the level of certain phenomena at some given period in comparison with the level of the same phenomena at some reference period. The index numbers are usually constructed for economic variables such as price, quantity, wage, unemployment, investment, cost of living, etc.

Index numbers are free from units of measurement because they show relative changes. For ease of understanding, index numbers are expressed in percentages. To construct index numbers at least two periods are required and a period that is economically stable and has no major crisis caused by wars, diseases, strikes, food shortage, etc. known as the normal period is selected as a base. Index numbers of wholesale prices and consumer prices, etc. are published by the Federal Bureau of Statistics and State Bank of Pakistan.

Uses/ Need of Index Number

There are many uses of index numbers but the most important are:

  • Many economic plans and Government policies depend on index numbers, for example, to control raising prices government import from the other countries or give subsidy (financial support) to the manufacturer.
  • Price index numbers are used to know the purchasing ability of money at different periods and places.
  • Quantity index numbers are used to know the changes in the quantities produced, consumed, sold, purchased, imported or exported, etc.
  • Consumer price index numbers are used to know standards of living of people and to know about the goods and services used by them.
  • Index numbers are used to forecast the future economic trends
  • Cyclical (long-term movements, which are in the form of oscillation) and seasonal (short term movement, which are linked with the seasons or movements which repeat themselves within a fixed period) movements are measured by index numbers.
Index Number

Shortcomings of Index Numbers

Index numbers can not be used freely due to the following shortcomings:

  • Improper base period give misleading results. Base periods must be free from all types of crisis caused by wars, diseases, strikes, or food shortage, etc. If such a period is not available then average of some or all the periods is selected as base.
  • Selection of favorite commodities is difficult because use of services and commodities by the individuals vary with the locality of people, social customs, standard of living, occupation, ideas of saving, courage of investment and sources of income, etc.
  • Quality of a product cannot be observed at each point, that is, ball to ball commentary is difficult. For example, if we want to view the quality of cloth at each thread before purchasing it becomes impossible.
  • Index numbers give rough measure of relative changes because sampling error or error of measurement may occur at the stages of gathering of data or base period may be improper or number of commodities may be less than required. According to Dr. Arriving Fisher the accuracy of index numbers may be increased by increasing the number of commodities.
  • Different methods of index numbers usually give different results.
  • Prices vary from place to place according to idea of profit of investors, expenditures on transportation and awareness about the psychology of buyers, hence their collection is difficult.

Miscellaneous Articles

 by 

Matrix Introduction

This post is about some basic introduction to a matrix.

Matrices are everywhere. If you have used a spreadsheet program such as MS-Excel, Lotus, or written a table (such as in Ms-Word) or even have used mathematical or statistical software such a Mathematica, Matlab, Minitab, SAS, SPSS and Eviews, etc., you have used a matrix. Let us start with the Introduction of the matrix.

Matrices make the presentation of numbers clearer and make calculations easier to program. For example, the matrix is given below about the sale of tires in a particular store given by quarter and make of tires.

 Q1Q2Q3Q4
Tirestone212032
Michigan5111524
Copper614728

It is called a matrix, as information is stored in a particular order and different computations can also be performed. For example, if you want to know how many Michigan tires were sold in Quarter 3, you can go along the row ‘Michigan’ and column ‘Q3’ and find that it is 15.

Similarly, the total number of sales of ‘Michigan’ tiers can also be found by adding all the elements from Q1 to Q4 in the Michigan row. It sums to 55. So, a matrix is a rectangular array of elements. The elements of a matrix can be symbolic expressions or numbers. Matrix [A] is denoted by;

Matrix

Row i of the matrix [A] has n elements and is [ai1, ai2, … a1n] and column of [A] has m elements and is Matrix Column

.

The size (order) of any matrix is defined by the number of rows and columns in the matrix. If a matrix [A] has m rows and n columns, the size of the matrix is denoted by (m x n). The matrix [A] can also be denoted by [A]mxn to show that [A] is a matrix that has m rows and n columns in it.

Each entry in the matrix is called the element or entry of the matrix and is denoted by aij, where i represents the row number and j is the column number of the matrix element.

Matrix of tire Sale

The above-arranged information about sales and types of tires can be denoted by the matrix [A], that is, This matrix has 3 rows and 4 columns. So, the order (size) of the matrix is 3 x 4. Note that element a23 indicates the sales of tires in ‘Michigan’ in quarter 3 (Q3).