Statistics Midterm PDF

Statistics What's Statistics? Statistics is a science that's discipline collecting analysing interpretation and presentation of data ‫يعني علم مبسط لتجميع وتحليل وتفسير وعرض البيانات‬ Descriptive statistics' It's organizing and summarizing Information by using Grap...

Statistics What's Statistics? Statistics is a science that's discipline collecting analysing interpretation and presentation of data ‫يعني علم مبسط لتجميع وتحليل وتفسير وعرض البيانات‬ Descriptive statistics' It's organizing and summarizing Information by using Graphs, charts, tables and calculations of various statistical measures to a set of data ‫االحصاء الوصفية هي أحصاء بتنظم وبتلخص المعلومه عن طريق جرافات او‬ ‫احصائيات او جداول او حسبابة لقيم احصائية لمجموعه من البيانات‬ Population? It's a collection of individuals, items or data considering statistical study ‫المجتمع او التعداد هو تجميعة افراد او اشياء او بيانات مع أعتبار الدراسة االحصائية له‬ Finite Population Finite numbers of the data or items or individuals inside of the population ‫تعداد محدود وهو رقم محدود يقدر عده من بيانات او افراد او اشياء‬ Infinite Population Infinite numbers of the data or items or individuals inside of the population ‫تعداد غير محدود وهو رقم ال يمكن عده من بيانات او افراد او اشياء‬ Population Size The number of items in population usually denoted by "N" ‫حجم التعداد هو عدد االفراد او البيانات او االشياء في التعداد وعادتا يرمز ليه‬ ‫" بالحرف‬N" Sample A sample is a part of population ‫العينه هي جزء من التعداد‬ Sample Size Number of elements in the sample denoted by N N ‫عدد العناصر ف العينه ويرمز ليه بحرف‬ Parameter It's a numerical quantity measuring some aspect of a population of scores ‫هي كمية عددية بتقيس طريقة عمل التعداد وهي عادتا ثابتة‬ Variable Variable is a characteristic of interest concerning the individual elements of a population or a sample ‫هي صفة ألهتمام او صفة تصف العنصر للفرد ف التعداد او العينه‬ :‫مثال‬ Gender "male/female" Family size "2/3/4/5" Quantitative variable: Quantitative variable is determined when the description of the characteristic of interest results in a numerical value ‫بأختصار المتحرك المعدود هو رقم متغير حسب نوع العينه او التعداد‬ ‫زي مثال عدد عائلتك بيختلف من عائلة لعائله ولكنه رقم معدود وفي نفس الوقت‬ ‫متغير من عائلة لعائلة‬ Types of Quantitative Variable: A discrete variable: A discrete variable is a quantitative variable whose values are countable. Discrete variables usually result from counting. a) Number of children in a family. b) Number of accidents per day in a city. ‫رقم كامل من غير فواصل كرقم اعضاء تعداد او غيره‬ A continuous variable: A continuous variable is a quantitative variable that can assume any numerical value over an interval or over several intervals. a) Height. b) Weight. c) Age. d) Income. e) Price. Etc. ‫رقم بفواصل كطول او كوزن‬ Qualitative variable: Qualitative variable is determined when the description of the characteristic of interest results in a non-numerical value. A qualitative variable may be classified into two or more categories a)Hair color. b) Blood group. c)Religion. Nominal variable: a) Religion b) Blood group c) ) Nationality Ordinal variable: a) Level of education b) Beauty ‫هي التعدادات ذو النوع الجودي حيث أن المتغير ال يكون رقم بل يكون قيمة غير عددية كلون الشعر او نوع الدم او غيره‬ Constant: A numerical characteristic which does never change or vary its value is termed as constant. π‫الثابت هو عدد او قيمة ثابتة غير متغيرة مثل ال‬ The value of π = 3.1416 is for all the circles. Frequency Table (For Qualitative Data) For qualitative data, in the frequency table, all the classes of the variables are mentioned along with their frequency, relative frequency and percent frequency. Relative frequency of a class = Frequency of that class Total number of observations Percent frequency of a class = (Relative frequency) * 100% The end of lecture 1 Data processing Chapter 2: Grouped data / ungrouped data (grouped data are in tables) (Ungrouped Data are individual items) 1,2,56,2,4 The mean: Mean The mean is the value which is derived by summing all the values and dividing it by the number of observations Computing Mean(Arithmetic mean) for Ungrouped Data Where, Xത = Mean , ∑ = Sum of a series of measures x = A raw score in a series of measures ∑ x = The sum of all the measures n = Number of measures 10,20,40,30 Geometric mean for ungrouped data The nth root of the product of the data values, where there are n of these. This measure is valid only for data that are measured absolutely on a strictly positive scale. Harmonic mean reciprocal for ungrouped data the reciprocal of the arithmetic mean of the reciprocals of the data values. This measure too is valid only for data that are measured absolutely on a strictly positive scale. Advantage of mean The mean is an average that considers all the observations in the data set. It is single and easy to compute, and it is the most widely used average. Disadvantage of mean Its value is greatly affected by the extremely too large or too small observation X 20 30 40 50 70 F 2 5 6 3 2 Mean for Grouped Data Xത = Mean, f = Frequencies, x = Midpoints of class intervals, Geometric mean, Harmonic mean for grouped data: 1,10,,5,6,7  ‫‪Chapter 2:‬‬ ‫‪Data processing‬‬ ‫يعني اكتر قيمة اتكررت‬ ‫‪In Ungrouped data:‬‬ ‫‪10, 22, 37, 46, 55, 61, 61, 61, 72,72,72 88.‬‬ ‫‪Mode= 61,72‬‬ ‫ممكن لو ارقام تانيه بنفس العدد ‪It can be more than one mode‬‬ ‫يضافوا عادي‬ ‫‪ bimodal‬لو كانوا اثنين بنسميهم‬ ‫‪ trimodal‬لو كانو ثالثة بنسميهم‬ ‫‪ multimodal‬اكثر من ثالثة نسميهم‬ ‫‪In Grouped Data:‬‬ W=Upper limit – lower limit W= 30 – 20 = 10 Quartiles: There are three quartiles, i.e. Q1, Q2 and Q3 which divide the total data into four equal parts when it has been orderly arranged. Q1, Q2 and Q3 are termed as first quartile, second quartile and third quartile or lower quartile, middle quartile and upper quartile, respectively. The first quartile, Q1, separates the first one-fourth of the data from the upper three fourths and is equal to the 25th percentile. The second quartile, Q2, divides the data into two equal parts (like median) and is equal to the 50th percentile. The third quartile, Q3, separates the first three-quarters of the data from the last quarter and is equal to 75th percentile. N= sum of frequencies Q3= (Sumf+1) X3=10.5  Chapter 3 Measure of dispersion Range: the range can be defined as the difference between the maximum value and the minimum value. R= H – S H= Highest value S= Smallest value