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### STATISTICS-AND-PROBABLITY-A-REVIEW-FOR-SHS.pdf

• 4. Descriptive Statistics - This includes the techniques which are concerned with summarizing and describing numerical data. This method can either be graphical or computational. - For easy understanding , tables , graphs and charts that display data are used
• 5. Inferential statistics  The technique by which decisions about statistical population , made based only on a sample having been observed or a judgment having been obtained. This kind of statistics is concerned more with the generalizing information or making inference about population.  Consist of generalizing from samples to population, performing hypothesis testing, determining relationships among variables and making predictions.
• 7. Terminologies Data- a set of observations, values, elements or objects under consideration Population (N)- complete set of all possible observations or elements. It consist of the total collection of observations or measurements that are of interest to the statistician or decision maker and about which they are trying to draw conclusion.
• 8. Sample (n)- Representative of a population. It is a collection of some , but not all , of the elements of the population under study in which the statistician is interested. Variable- attribute of interest observable on each entity in the universe. It is a characteristic which may take on different value like sex, weight, income, size, ages, IQ, sales and temperature.
• 9. Dependent Variable – it is the value affected by change in other factors and is called the criterion variable. Independent Variable – its changes caused other variables to change in value and is called the predictor variable. Tabulation – the process of classifying or grouping scores in the systematic arrangement.
• 10. Con’t Ungrouped data – data which have not been organized or classified and usually exhibit no pattern. Parameter – is the characteristics of population which is measurable. Frequency distribution – the tabulation of scores or measures group with class intervals. Class Frequency – it is the number of measures of observations in an interval
• 11. Class Intervals or Stated Class Limits – these are classes or ranges of values that the observations can assume. Each class interval has a lower limit and an upper limit. Class Boundaries or Real or Exact Class Limits – these are the exact values of class limits by at least 0.5. It is the upper limit of one class and the lower limit of the succeeding class.
• 12. Class Mark – it is the midpoint of a class interval in a frequency distribution and taken as the average of the lower and upper limits. Class Size – it is the width of class intervals and measures the interval between the first value of one class and the first value of the next class. Continuous Data – data that may progress from one class to the next without a break and may be expressed by either whole number or fractions. Discrete Data – data that does not progress from one class to the next without a break.
• 13. Con’t Frequency Polygon – a graph which is constructed by connecting points above the midpoint of a step and the height equal to the frequency of the steps. Histogram – a frequency curve which aims to composed of a series of rectangles constructed with the steps as the base and the frequency as the height.
• 14. Population and Samples  Population is a set of people or objects you are interested in a particular study.  - Finite population or infinite population  Examples :  finite – set of high school principals , senators , congressman  Infinite population – set of all people in the Philippines
• 15. Population and Sample Population Sample Sample Statistics Population Parameters Statistical Inference
• 16. SUBSCRIPT AND SUMMATION NOTATIONS Subscript is a number or letter representing several numbers placed at the lower right of a variable. Summation symbol ∑ ( Greek capital letter “ sigma “ ) is used to denote that subscripted variables are to be added.
• 17. Xi stands from x1 , x2 , x3 , … . Xn = ( X1 ) + ( X2 ) + ( X3)+ … + ( Xn ) ෍ 𝑖=1 3 ෍ 𝑖=1 𝑛 𝑋 Read as “ the summation of the x’s from I to 3 .
• 18. Examples: 1. 2. ∑ 5 i=1 = x1 + x2 + x3 + x4 +x5 ∑ 35 i=22 = xi xi x22 + x23 + x24 + … + x35
• 20. Chapter 2 . Collection of Data  Two types of data 1. Primary – are information collected by a person or organization that will be using the information. This are first – hand or original sources. 2. Secondary – are information already collected by someone else. Are information take from published or unpublished data previously gathered.
• 21. Methods in Collection of Data  Direct or interview method  Indirect or questionnaire method  Registration method  Observation Method  Experiment Method
• 22. Sample Population (Parameter) μ (mu) Sampl e Statistic x N n = 1 +N(e)2 Where: n- sample size N- population size e- margin of error
• 23. Given: Population = 25,000 margin of error 5% (.05) Solve for the sample size (n) 25,000 n= 1 + (25,000) (0.05)2 25,000 n= 1 + (25,000) (0.0025) 25,000 n= 1 + 62.5 25,000 n= 63.5 n= 393.70 say 394 or 400
• 24. Sampling Techniques 1. Simple Random Sampling (SRS)- most basic method of probability sample, assigns equal probabilities of selection to each possible sample. Equal chance of being selected. ▪ Lottery or fishbowl sampling ▪ Table of Random Numbers ➢ SRS without Replacement- drawn papers are no longer returned ➢ SRS with Replacement- allows repeats in selection
• 25. Continuation of Sampling Techniques 2. Systematic Sampling – it is assumed that the members of a population are arranged in a specific order. Population Systematic Sample
• 26. Systematic Sampling  For a population of N element where n units will be taken. Let K = N / n. For example: 50- students in a class whose names are arranged alphabetically , 10 students are to be taken as sample. K = 50 / 10 = 5. Suppose from the first 5 , the 3rd student is chosen at random. 3rd , 8th , 13th , 18th … 48 or if every 5th member is selected, samples consists of 5th , 10th , 15th and so on.
• 27. Types of Systematic sampling 3. Stratified Random Sampling ➢ The universe is divided into L mutually exclusive Sub-universe called strata Population Stratified Random Sample ➢ Independent Simple random samples are Obtained from each stratum a b c d
• 28. Stratified Random Sampling  The sample size should be proportional to the size of the stratum in the population. Suppose in the class of 42 students , 18 boys and 24 girls. If a sample of 14 students be chosen such the number of boys and girls are proportionally represented. Boys = 18 ( 14 ) = 6 boys 42 Girls = 24 (14 ) = 8 girls 42
• 29. Stratified Random Sampling Obtain a sample of 100 students proportionally representing each level. Level Number of Enrollees Freshmen 500 Sophomores 420 Juniors 360 Seniors 300 Total
• 30. Continuation of Sampling Techniques 4. Cluster Sampling P Provinc e Town Town Town Town Barang ay Barang ay Barang ay Barang ay Barang ay Barang ay
• 31. 4. Cluster Sampling - can be done by subdividing the population into smaller units selecting only at random some primary units where the study would then be concentrated. Sometimes it is referred to as “ area sampling “ because it is frequently applied on a geographical basis
• 32. Continuation of Sampling Techniques ❖ Non- Random Sampling ▪ Purposive Sampling ▪ Quota Sampling ▪ Convenience Sampling
• 33. Chapter 3. Presentation of Data  Textual presentation  Tabular presentation  Graphical presentation ▪ Statistical Table Table Number and Heading Stub Head Master Caption Column Caption Column Caption Column Caption Column Caption Box Hea d Body
• 34. Graphical  Bar Graphs – Vertical Graph 0 1 2 3 4 5 6 Series 1 Series 2 Series 3
• 35. Horizontal Bar Graph 0 2 4 6 Category 1 Category 2 Category 3 Category 4 Series 3 Series 2 Series 1
• 36. Line graph 0 1 2 3 4 5 6 Category 1 Category 2 Category 3 Category 4 Series 1 Series 2 Series 3
• 37. Pie Chart Sales 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
• 39. Copyright © 2000 by Monica Yuskaitis Vocabulary Review • Sum – the answer to an addition problem. • Addend – the numbers you added together to get the sum. 6 + 9 = 15
• 40. Copyright © 2000 by Monica Yuskaitis Definition Mean Means Average
• 41. Copyright © 2000 by Monica Yuskaitis Definition • Mean – the average of a group of numbers. 2, 5, 2, 1, 5 Mean = 3
• 42. Copyright © 2000 by Monica Yuskaitis Mean is found by evening out the numbers 2, 5, 2, 1, 5
• 43. Copyright © 2000 by Monica Yuskaitis Mean is found by evening out the numbers 2, 5, 2, 1, 5
• 44. Copyright © 2000 by Monica Yuskaitis Mean is found by evening out the numbers 2, 5, 2, 1, 5 mean = 3
• 45. Copyright © 2000 by Monica Yuskaitis How to Find the Mean of a Group of Numbers • Step 1 – Add all the numbers. 8, 10, 12, 18, 22, 26 8+10+12+18+22+26 = 96
• 46. Copyright © 2000 by Monica Yuskaitis How to Find the Mean of a Group of Numbers • Step 2 – Divide the sum by the number of addends. 8, 10, 12, 18, 22, 26 8+10+12+18+22+26 = 96 How many addends are there?
• 47. Copyright © 2000 by Monica Yuskaitis How to Find the Mean of a Group of Numbers • Step 2 – Divide the sum by the number of addends. 6)96 sum # of addends 1 6 36 6 6 3
• 48. Copyright © 2000 by Monica Yuskaitis How to Find the Mean of a Group of Numbers The mean or average of these numbers is 16. 8, 10, 12, 18, 22, 26
• 49. Copyright © 2000 by Monica Yuskaitis What is the mean of these numbers? 7, 10, 16 11
• 50. Copyright © 2000 by Monica Yuskaitis What is the mean of these numbers? 2, 9, 14, 27 13
• 51. Copyright © 2000 by Monica Yuskaitis What is the mean of these numbers? 1, 2, 7, 11, 19 8
• 52. Copyright © 2000 by Monica Yuskaitis What is the mean of these numbers? 26, 33, 41, 52 38
• 53. Copyright © 2000 by Monica Yuskaitis Definition Median is in the Middle
• 54. Copyright © 2000 by Monica Yuskaitis Definition • Median – the middle number in a set of ordered numbers. 1, 3, 7, 10, 13 Median = 7
• 55. Copyright © 2000 by Monica Yuskaitis How to Find the Median in a Group of Numbers • Step 1 – Arrange the numbers in order from least to greatest. 21, 18, 24, 19, 27 18, 19, 21, 24, 27
• 56. Copyright © 2000 by Monica Yuskaitis How to Find the Median in a Group of Numbers • Step 2 – Find the middle number. 21, 18, 24, 19, 27 18, 19, 21, 24, 27
• 57. Copyright © 2000 by Monica Yuskaitis How to Find the Median in a Group of Numbers • Step 2 – Find the middle number. 18, 19, 21, 24, 27 This is your median number.
• 58. Copyright © 2000 by Monica Yuskaitis How to Find the Median in a Group of Numbers • Step 3 – If there are two middle numbers, find the mean of these two numbers. 18, 19, 21, 25, 27, 28
• 59. Copyright © 2000 by Monica Yuskaitis How to Find the Median in a Group of Numbers • Step 3 – If there are two middle numbers, find the mean of these two numbers. 21+ 25 = 46 2)46 23 median
• 60. Copyright © 2000 by Monica Yuskaitis What is the median of these numbers? 16, 10, 7 10 7, 10, 16
• 61. Copyright © 2000 by Monica Yuskaitis What is the median of these numbers? 29, 8, 4, 11, 19 11 4, 8, 11, 19, 29
• 62. Copyright © 2000 by Monica Yuskaitis What is the median of these numbers? 31, 7, 2, 12, 14, 19 13 2, 7, 12, 14, 19, 31 12 + 14 = 26 2) 26
• 63. Copyright © 2000 by Monica Yuskaitis What is the median of these numbers? 53, 5, 81, 67, 25, 78 60 53 + 67 = 120 2) 120 5, 25, 53, 67, 78, 81
• 64. Copyright © 2000 by Monica Yuskaitis Definition Mode is the most Popular
• 65. Copyright © 2000 by Monica Yuskaitis Definition • A la mode – the most popular or that which is in fashion. Baseball caps are a la mode today.
• 66. Copyright © 2000 by Monica Yuskaitis Definition • Mode – the number that appears most frequently in a set of numbers. 1, 1, 3, 7, 10, 13 Mode = 1
• 67. Copyright © 2000 by Monica Yuskaitis How to Find the Mode in a Group of Numbers • Step 1 – Arrange the numbers in order from least to greatest. 21, 18, 24, 19, 18 18, 18, 19, 21, 24
• 68. Copyright © 2000 by Monica Yuskaitis How to Find the Mode in a Group of Numbers • Step 2 – Find the number that is repeated the most. 21, 18, 24, 19, 18 18, 18, 19, 21, 24
• 69. Copyright © 2000 by Monica Yuskaitis Which number is the mode? 29, 8, 4, 8, 19 8 4, 8, 8, 19, 29
• 70. Copyright © 2000 by Monica Yuskaitis Which number is the mode? 1, 2, 2, 9, 9, 4, 9, 10 9 1, 2, 2, 4, 9, 9, 9, 10
• 71. Copyright © 2000 by Monica Yuskaitis Which number is the mode? 22, 21, 27, 31, 21, 32 21 21, 21, 22, 27, 31, 32
• 72. Copyright © 2000 by Monica Yuskaitis Definition Range is the distance Between
• 73. Copyright © 2000 by Monica Yuskaitis Definition • Range – the difference between the greatest and the least value in a set of numbers. 1, 1, 3, 7, 10, 13 Range = 12
• 74. Copyright © 2000 by Monica Yuskaitis How to Find the Range in a Group of Numbers • Step 1 – Arrange the numbers in order from least to greatest. 21, 18, 24, 19, 27 18, 19, 21, 24, 27
• 75. Copyright © 2000 by Monica Yuskaitis How to Find the Range in a Group of Numbers • Step 2 – Find the lowest and highest numbers. 21, 18, 24, 19, 27 18, 19, 21, 24, 27
• 76. Copyright © 2000 by Monica Yuskaitis How to Find the Range in a Group of Numbers • Step 3 – Find the difference between these 2 numbers. 18, 19, 21, 24, 27 27 – 18 = 9 The range is 9
• 77. Copyright © 2000 by Monica Yuskaitis What is the range? 29, 8, 4, 8, 19 29 – 4 = 25 4, 8, 8, 19, 29
• 78. Copyright © 2000 by Monica Yuskaitis What is the range? 22, 21, 27, 31, 21, 32 32 – 21 = 11 21, 21, 22, 27, 31, 32
• 79. Copyright © 2000 by Monica Yuskaitis What is the range? 31, 8, 3, 11, 19 31 – 3 = 28 3, 8, 11, 19, 31
• 80. Copyright © 2000 by Monica Yuskaitis What is the range? 23, 7, 9, 41, 19 41 – 7 = 34 7, 9, 23, 19, 41
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