discrete and continuous data pdf

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discrete and continuous data pdf

Therefore, if f (x) is the PMF of x , then CDF is given as. It could be 9.57. Ex 1 & 2 from MixedRandomVariables.pdf. Each assignment does have an answer key that will be available. stream stream X takes any single given value is zero: P(X=c)=0 Probabilities for a continuous … endobj Some of the worksheets for this concept are Stat 243 week 1 recitation work name key, Discrete and continuous variables, Discrete and continuous domains, Discrete vs continuous notes, Discrete and continuous domains, Data types, Mathswatch clip 63 data, Discrete and continuous random variables. 77 0 obj Continuous data are data where numbers between any two data … discrete data set and a continuous (scalar or vector) data set, using a similar approach to that of Ref. Access the Discrete v. Continuous PowerPoint file. Continuous data. x^��r"1C��%w2�:S��jɲHվ��P��B�R~ն�M�m�V�@%iӦm� *A�Uk�=��£U[�,��E��rJ��'%�=6�l�f�� %V҈`�XO��V�${6o��Q(B�|#�9�E��\��R%�L؝�H^��4�iz�E�)N�� B�I��R�*M��F �њ� �� Pg��h�%�L�� 2h��TZ8��}�u�u��ү߫3j,��Y�٘�q0��#%��? 4 0 obj PDF (679.68 KB) This assignment provides a wide variety of discrete & continuous data questions that will help students to better understand the topic and challenge them.This worksheet is one example of our assignments. >> Following established practice [2] our estimator constructs bins of different sizes so that each bin has n data points inside it (n is a parameter set by the user). T�6m�V�@%iӦm� And Numerical Data can be Discrete or Continuous: Discrete data is counted, Continuous data is measured . type of data in which separate items are counted. Discrete Data can only take certain values. 1. Working With Dates 1 Discrete Data Continuous Data • Separate and distinct data • Can only take on certain values in T�6m�V�@%iӦm� Comparing discrete and continuous data. Here the possible set of outcomes are {1,2,3,4,5,6}. T�6m�V�@%iӦm� !!Qualitative!!Discrete! %PDF-1.4 Determine if the following set of data is discrete or continuous… Mixture of Discrete and Continuous Random Variables What does the CDF F X (x) look like when X is discrete vs when it’s continuous? I hope this post helped you with random variables and their probability distributions. stream For example: Your weight. endobj Videos, worksheets, 5-a-day and much more The numerical data used in statistics fall in to two main categories. 1. While a discrete PDF (such as that shown above for dice) will give you the odds of obtaining a particular outcome, probabilities with continuous PDFs are matters of range, not discrete points. T�6m�V�@%iӦm� 1 The number c of calories consumed is a function of the number b of bars eaten. Source; PubMed; Authors: Brian C Ross. This assignment provides a wide variety of discrete & continuous data questions that will help students to better understand the topic and challenge them.This worksheet is one example of our assignments. 14 could have a continuous component and a discrete component. Before you do anything with the data you’ve collected, you must label your variables as either discrete or continuous. 2. DISCRETE AND CONTINUOUS PROBABILITY DISTRIBUTIONS Probability mass functions If x ∈ {x 1,x 2,x 3,...} is discrete, then a function f(x i) giving the probability that x = x i is called a probability mass function. <> 1 discrete or continuous? February 2014; PLoS ONE 9(2):e87357; DOI: 10.1371/journal.pone.0087357. >> <> Difference between discrete and continuous data. rz �;�hﮰwW踫* ��W�iT�� {!θuvpa�Zy��I$�9��!p��}g�J�*�1)�V�r�a,&�r5xp��ђ&��0`F.a�`';�ή�'��?��qo�Ǐ��K��;O�ֺJ˞��n�[>��z�vǆ�{��~6�W� �)��L*f�fR5��c�3�&2�T�DמX\s &6=f�)�qDR�AK��Љ2{У�^��Nbw�B �@�d��;K�K�w⼊�}�}`V�_ňkF��ԭÁ�_b�q��i�zj3i� � h�#��m͈6bՆ��YcN�q䒖Q��@4$rz3W4?aEk#�/i��\|��ջ� 5�PИ$��Y�� "_�Η��&.J9��w_>�})�x��\#/]�0�D~X,� ]��j��8��g� �4P��)'��IRx�1"' �u�E�z�z3�`v��U�p�9�J{W�_@��a�D�� I�� gEO�,D AY��|p The data we've looked at, throughout this course, have had a fixed range of values. x�c``��? 3. T�6m�V�@%iӦm� �Da�&" �@@fy�TSDZl� 4��(�Hy+�2v�)p%:�eB�m�D@�X&��Z�Lb��hk-H�X&��(�q��Ԛ��\�&��j�v)��zw �ǁ�" x��SYtKR�zh�˳��-i1Jk�~~��W8s�N��Rx��+�=��2��L�~�$��X�A��\�D�hM�A��G��7R.� �0��LtJ��ac��92:=uf�Hq9722ECg��!M�7n�߭n]i�0o��΅J3�D�E��Ͻϫt��q:�'��p/��sM�|��z�:�1� @vt�r�955*�m�S��I�0�u�z�� q��H�H/%��O�~�NߡW��k��yj8Rre��. "��`��%*4��|s��8&�� (�ĺ�j� ��26;� ̪�^ It’s density function is: • where µ and σ are specific parameters of the function. /ExtGState<> This data is known as, Discrete Data. (e) The number of miles per gallon (1) 4.!There are 40 sheep on a farm. And continuous random variables, they can take on any value in a range. Each assignment does have an answer key that will be available. 1249 1. In this lesson, we'll explore the difference between discrete and continuous data. ֗��O�%X�-��T��z It could be 9.58. I've changed the random variable now. Such a function must have the properties that f(x i) ≥ 0, for all i, and X i f(x i) = 1. endobj 2 0 obj ;��.�Qv��]s�ޒ�:S%#yqp�&1�u2�?��L��/775M��OM?��x�3u��}�m}�� So we call it an infinite set of outcomes. Learn vocabulary, terms, and more with flashcards, games, and other study tools. endstream T�6m�V�@%iӦm� Continuous and Discrete Modules, eBook pdf (pdf eBook) von Saad H. Mohamed bei hugendubel.de als Download für Tolino, eBook-Reader, PC, Tablet und Smartphone. 1. PDF for the above example. 2. Data is the most salient entity in statistics as it is necessarily the “study of the collection, organization, analysis, and interpretation of data”. Problem 1: Discrete versus Continuous Variables. This data is known as, Discrete Data. Be able to construct a Bayesian update table for continuous hypotheses and continuous data. T�6m�V�@%iӦm� Fill in the table below with your answer and, … A r.v. <> Working With Dates 1 Discrete Data Continuous Data • Separate and distinct data • Can only take on certain values in 3. 81 0 obj Example 2. T��M[-�mr�$�kx"�g T��r��$�q��H��0%p؁%��ɐ�6��ǽ��*^�4�1P"��}K�?8^��R z쿁� gn��[��7�n{0� Data can be measured (such as length or weight) or numerical (basically numbers). That data can be presented in different ways. Students can add their o. A race can be timed to a millisecond. Flipchart to structure lesson with links to short videos etc. We are not talking about random variables that are polite. While there are many exciting and stimulating real time data web sites available for classroom use, these resources should NOT replace opportunities for students to collect data themselves through hands-on experimentation. Binning methods make the data completely discrete by grouping the data points into bins in the continuous variable y, as shown in Figure 1D. stream Discrete data is information that can be counted. Qualitative vs quantitative, discrete vs continuous. stream 1 0 obj For example, there is clearly a 1 in 6 (16. Explain. • Continuous – Normal • Discrete – Binomial – Poisson . Discrete versus Continuous Data Page 2 solvers need to be conscious of their own reasoning processes by talking or writing down their thoughts (Lockhead 1981). <> 29 0 obj The data we've looked at, throughout this course, have had a fixed range of values. endobj Multiple imputation of discrete and continuous data by fully conditional specification @article{Buuren2007MultipleIO, title={Multiple imputation of discrete and continuous data by fully conditional specification}, author={S. van Buuren}, journal={Statistical Methods in Medical Research}, year={2007}, volume={16}, pages={219 - 242} } Discrete Data and Continuous Data • A set of discrete data can include only certain values. We can split them further into con-tinuous variables and discrete variables. The numerical data used in statistics fall in to two main categories. Discrete data is graphically represented by bar graph whereas a histogram is used to represent continuous data graphically. Continuous You are traveling over winter break on a plane from Austin Intercontinental Airport (AUS) to Los Angeles, California (LAX), describe 3 discrete and 3 continuous data examples you might encounter during your trip: Discrete Examples Continuous Examples 1. <> x�c``��? (a) The length (1)! As it is taking a value from an infinite set, we call it a continuous random variable. x�͘Mo�F�ȍ�h�I{�fgf?��)� Ŷl'EnE��$=��,E��Z. This quiz will help you see how well you understand discrete and continuous data through the use of word problems. z�OC��]��Zay4��_k�ЯU�� ahn��x��B�4��i�#@E)Ƣ��-p��c��h��QUCu��rՈsp8��P��0��X��g��n��0�d�I�y��e��"B��.��+d�`k��-��(�e��ҋK�2��L��[��Q�. %�� f(x) 3. ]��+�e�tF^�޷м�T%�ɵ]]��!n0��e��[��n��f�;8�B��BiUJ*�juB7�� Z\��&)�hy�k_ڻ��}��ǂ��x�,yg-�6�Gk�dP��[F-H�c�8[��4j�0�Z˓T6E�@�G��s�v)��R�ޡ��hg�cY��{!U��Hmf�[?��z�{��l]�C�e��f�B+��V��c� ͫ��I_+mJ��p� ��j֡חB�u��>O�I�'��$f�)��Vy��E3g�@�ߴD��L��x�;]z�a�[�?�_�� CDF for Discrete random variable. By quantitative, I mean that they can take a range of numeric values that measure something in the real world. For discrete data, numbers between two data values will make no sense. 3. Discrete Data. T�6m�V�@%iӦm� D �O5��S�̝�T��D��/�mY�G ͋wn��u��ఠ��9��M=m�/ѣ��9o��@p�0��{��@ �B�@��H��v�ǁaJ�=J �K۸kt��Jr�9��}��m�u�3�MJ5�9_�$�&ӎ?��υ��z��ߒ,V��@�`�sw\�Nr�46G@0-ՠ��hs^�`��쎀��6�e��V�=�O�n��G ��o}cj�+�&L$�\��Уж��m�rULێRz��yT1m;J��>�6*�Q��m{��K=��)^��A$�>mS�kb3�ͪd(�^b��C�~w��@[��9N��!�m؂H'�} �綽�N��WZP�;V:�1��ɳ��Q�4i�`.��}ND�-F5�� |ٽ��n��G]s��=�x��Bp/%b1�6"��)0w�� ODn�y��뎟��ؽR�k`�?$=wl��^%��{�o�� :�`��`=GI��("�;� H2aAE�9��> �`|t$��?t�ĝߑp��dr�I��geGP@�*��i[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PI� � Discrete random variable:If a random variable can take a discrete value from a finite set of outcomes, then we call it a discrete random variable. 6 %) chance of rolling a 3 on a dice, as can be seen in its PDF. Did the figure above helped you understand the difference between discrete and continuous data? 4 0 obj A r.v. %�� endstream Data Activity In this activity students will review examples of data to deduce which types of data are more helpful in different situations. The difference between discrete and continuous variable can be drawn clearly on the following grounds: The statistical variable that assumes a finite set of data and a countable number of values, then it is called as a discrete variable. Continuous data is usually recorded as grouped data so is usually represented by histograms or cumulative frequency graphs. T�6m�V�@%iӦm� 30 0 obj Displaying top 8 worksheets found for - Discrete And Continuous Data. of a continuous random variable differs from the definition for the p.m.f. Data is the most salient entity in statistics as it is necessarily the “study of the collection, organization, analysis, and interpretation of data”. Sketch and doodle notes allow for students to stay focused, grasp new concepts and retain information. X can take an infinite number of values on an interval, the probability that a continuous R.V. The Corbettmaths Textbook Exercise on Continuous/Discrete Data. 28 0 obj Statistical Methods in Medical Research 2007; 16: 219–242 Multiple imputation of discrete and continuous data by fully conditional speciﬁcation Stef van Buuren TNO Quality of Life, Leiden, The Netherlands and University of Utrecht, i�ﱒdi|,�@�ڎ�L�4��@(��e��3yPcb1��yJ��γd�7�q}n��lv܂��+'��ʉR�x� Continuous R.V.’s have continuous probability distributions known also as the probability density function (PDF) Since a continuous R.V. Continuous and discrete numbers T HE BEST PLACE TO START learning about data vi-sualisation is with quantitative variables. ; Continuous data can take any value, including decimals. Notice that, when b = a, there is P(x = a) = Z a a f(x)dx = 0. Your weight is not a specific fixed number. Section 4.2 Discrete and Continuous Domains 157 EXAMPLE 2 Graphing Continuous Data A cereal bar contains 130 calories. <> We call these continuous data and discrete data. 1. 916 You'll also be tested on how well you know the definitions of certain types of data. Ex 1 & 2 from MixedRandomVariables.pdf. By and large, both discrete and continuous variable can be qualitative and quantitative. f(x) may be deﬁned such that the probability of the event a < x ≤ b is given by P(a < x ≤ b) = Z b a f(x)dx. Flipchart to structure lesson with links to short videos etc. The 6 minute half mile time is continuous data; the number of people trying out for the team is discrete data. between discrete (snapshots) and continuous and real time data. stream Continuous data is measured. Continuous data can take on any value as it’s measured. Is the domain of the graph discrete or continuous? x�ݙKo�6� �K��@�v�ߏk��cklǏl��@�i��3#ɒ%ْ_��0"S$=$��Tf>2�6sVq��?�SoW�ZF�n5��Ff��T�t��QQI/��:fҪ��q <> Continuous data. On the other hand, continuous data includes any value within range. For example: height and time. Visually, this can be depicted as a smooth graph that gives a value for every point along an axis. That is not what we're talking about. 2 Introduction 2. 2. Discrete Probability Distributions If a random variable is a discrete variable, its probability distribution is called a discrete probability distribution. 79 0 obj 'h��Ngr��D-�*sl>��/��)|�Z�x�;�q � ��o� ��)��kL��F��l�-k�('�ImQP�IO��T��.>��Ǽv�Խ.�oU0��>��,�F��'�{S��C��Ю�fLk �BeX� :�L��̑�~��l[I��W�V0U��4l�~�+��Ngf��ua`��/��˫��t��7�a��_:T��6v ��T��h��h�%X5��mS��`� �n&�@�9��2J( ��Ë{7�;��OV��v�m�G:�첦g�c��t�7��(�)lPt�Yf�w��cl"2��&R��t��tʳ��3A@��Fz�L��DpA��x�0Y��,�y��c��/�e��߳֟QѮ7��Sk��v�J��:�;��r�VUH�Q��)}�X��?U�Q�k�Am��N��a{uw��~x�j��,��p� C#��)��^�9��/��W�#�:R��. They are discrete data and continuous data. endobj 60 0 obj Discrete vs continuous: Discrete data can only take certain values, for example: favourite colours or age in years. Graph the function. Qualitative vs quantitative, discrete vs continuous. )�(� #8�BׄA(��M2��$�I�҂x|��9N Մ\��Zŵk� Continuous data is usually recorded as grouped data so is usually represented by histograms or cumulative frequency graphs. Be able to recognize the pdf of a normal distribution and determine its mean and variance. T�6m�V�@%iӦm� ... a random variable where the data can take infinitely many values and the sum of the probabilities is 1. could have a continuous component and a discrete component. EXAMPLE: Integers from 1 to 5 −2 −1 0123456 A continuous domain is a set of input values that consists of all numbers in an interval. What is discrete data? Ticket out the Door – Discrete vs. >> endobj )9�AP\.�wg�� x��?� Be able to construct a Bayesian update table for continuous hypotheses and continuous data. � 2. T�6m�V�@%iӦm� Ex: Rolling a dice. Example. Discrete vs Continuous Data . 2. T�6m�V�@%iӦm� 3. endstream 3. We have not yet encountered data that could take any value within a defined range, known as, Continuous Data.. (c) The number of seats (1)! endobj They are discrete data and continuous data. �o4RfK��h�)�(6��.��Q�.��YD� Well now, we can actually count the actual values that this random variable can take on. ... Probability density function of a continuous random variable (pdf) - NOTATION. As they are the two types of quantitative data (numerical data), they have many different applications in statistics, data analysis methods, and data management. T�6m�V�@%iӦm� Discrete vs Continuous Data . Determine if the following set of data is discrete or continuous: The heights of your classmates. PowerPoint quiz - identify whether discrete or continuous. T�6m�V�@%iӦm� Tabulation of discrete data, done against a single value, is called as an ungrouped … This is an important statistic x��ZIo�F&�Q�0�=�P )P�g_��j˖�4qOE��S89��{�E"E��JA��ћ�{�P��8>"S.�J0��Rg,�&��̨H��g'��T0oyѥ��Hf��.0n��]ѳ��\0�8\�(:��$�,=>�6{�)��.S/�V"d�1�=�F@��~��}��]��!\�.��+ �|�9��BqD�t1�ObVm��-k�8�Ǚ��+&0�r��^5��;��w�6�1�c">��m�-�X� �1�ǂ��7�τ��w�HA�ƫL)I�%P The 6 minute half mile time is discrete data, and the 6th place ranking is continuous. While continuous-- and I guess just another definition for the word discrete in the English language would be polite, or not obnoxious, or kind of subtle. Consider x ∈ {0,1,2,3,...} with f(x) = (1/2)x+1. 1. A bar graph or pictograph would be wise choices to demonstrate discrete data … T�6m�V�@%iӦm� Did we mention that they're 100% free? This can be visually depicted as a bar chart. !Put a cross in the box to indicate whether each of the following is discrete or!continuous data.! 58 0 obj <> !^,�7i8�Qr�i;Fj��ө;F$ܦ�tn��1:t��-��) ��͖9��+.U'�Q�?᷇�+\��}�)��p�c��t��9�q��4mLG��H�љ�S�4��);Z��gf��3A��觎N��$鈢��,s�.��1��'��8� ��3!\�m�mK��˲��\�N��R�>�S��q�{��z��)�O�6�BE0$��1��v�L��M�O�ޮ�s�qk�=�;G�w�0��H�̦��H��g�흂��}��o�ͻc�!FY�N�V��DJ�=O&㙉B�N�T�`��7��7�x��e�%e��!�D��y��eh��Ӗ_I�n]��7w� S�s�u8ܱ��D��(�I�,y�w��k(�|0�d��}�#1�*_ For example, a set of data that describes the value of Canadian coins in people’s pockets can include the values 70¢, 10¢, and 5¢, but it can’t include the values 1¢ and 2¢, since the smallest Canadian coin is a nickel. Comparison Chart: Discrete Data vs Continuous Data. endobj 2. 61 0 obj We can compare discrete and continuous data by looking at how water comes out of a tap. Time in a race. 1011 M2ɓf�m�0��J8�/�p!�т[�$��e��_�5Խz��,)�rdS/$�+p4"��{"�� 3. <> Discrete and Continuous Domains A discrete domain is a set of input values that consists of only certain numbers in an interval. cG��+�M�-�:�ތ~��UEmUQ|˭_:�l�� endobj PDF (1.06 MB) This resource is the answer key to the free download "Discrete & Continuous Data Wks". Suppose you … Key Differences Between Discrete and Continuous Variable. View Working With Dates.pdf from IT 13203 at City University of Hong Kong. Get your practice problems in Discrete v. Continuous Data here. This is a type of data that <> endobj T�6m�V�@%iӦm� Mutual Information between Discrete and Continuous Data Sets. 1. So let me delete this. Some of the worksheets for this concept are Stat 243 week 1 recitation work name key, Discrete and continuous variables, Discrete and continuous domains, Discrete vs continuous notes, Discrete and continuous domains, Data types, Mathswatch clip 63 data, Discrete and continuous random variables. Continuous data is measured. Continuous Data Continuous data makes up the rest of numerical data. endobj %PDF-1.5 stream Discrete vs continuous: Discrete data can only take certain values, for example: favourite colours or age in years. endstream Start studying Discrete + Continuous Random Variable. Cards to sort into two groups - may think of any way to split. In this lesson, we'll explore the difference between discrete and continuous data. Your weight can be any weight within the range of human weights. We're talking about ones that can take on distinct values. 27 0 obj T�6m�V�@%iӦm� <>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> /Length 79 0 R stream Continuous data can take on any value as … endstream Show Answer. PowerPoint quiz - identify whether discrete or continuous. Continuous Data with Continuous Priors Class 14, 18.05 Jeremy Orloﬀ and Jonathan Bloom. Continuous Data with Continuous Priors Class 14, 18.05 Jeremy Orloﬀ and Jonathan Bloom . ?Wy? Cards to sort into two groups - may think of any way to split. Discrete vs Continuous Notes 2 Discrete data usually occurs in a case where there are only a certain number of values, or when we are counting something (using whole numbers). What is the difference between discrete and continuous data? Discrete data usually involve counting a number of items, such as the number of books, computers, people, and so forth. Example 3. Continuous data is information that can be measured at infinite points. T�6m�V�@%iӦm� T�6m�V�@%iӦm� 8��З��N�mU��|8�R`Wd�q{Gv��L��*n��;p��$��T4-*,��Bc��m萓�rmlY�_E�"��ʩWKt��K��V��!�+Z;f�(�[�J��V7C��̳"�6�y��kj,�k�m��d��:�:��UMVЭ�PT�5�\S��4T1,:GrL�Мz�@��gC��_`��[��vȡF`R��yL�,��x�]��Ƴ��WF�P}š7�N�Q ��˚�,*�y�a2/r�Y3�il��]��V��>t��5�i�9Ţ�1�i�4� Discrete data is countable while continuous data is measurable. discrete variable. Example: the number of students in a class. endobj endobj However, these two statistical terms are diametrically opposite to one another in the sense that the discrete variable is the variable with the well-defined number of permitted values whereas a continuous variable is a variable that can contain all the possible values between two numbers. Showing top 8 worksheets in the category - Discrete Vs Continuous. *��h�a��TP�� T�6m�V�@%iӦm� 2. endstream endobj DOI: 10.1177/0962280206074463 Corpus ID: 15640743. We call these continuous data and discrete data. All random variables, discrete and continuous have a cumulative distribution function (CDF). stream Determine if the following set of data is discrete or continuous: The number of books on your shelves. Similarly if x is a continuous random variable and f (x) is the PDF of x then, CDF for Continuous random variable. If not keep reading! �4V��R ��@�[>�?��3�R6��MO�P��\ߕ��=��gˡ��ΑS!4f�&O1�[�q�+�c�L(��@�K��3��օ��4}�|�%_�0�3�EDӨ/�0'��ߠn(�~�0� n`�4�Ѧ@im��2 ��a�i0��{|��w��J&�"Y&��&��i��)��_�g9t=��L~NF�B�� Uu�7��x�xB�0�N�8�2�#�i.0��zh��L��hN�-��/p[ϧ��$��MHc�&�I�6��Fv��; v�\�z��>P�hf3 �:�Y��$ce��P$�m1L��vV�)#Dc5�S.Q��5 �� nn�8D��Ur��2��CV3�� rRZ]�I��ȃ�Hvԅ�j� jL��Y�~ˈ�yL0N��5��WVN;�� ޥB��ַ��=�~�ۚ�`.u4��K��H"�x"�i4�U�NOo��57�C[�w��;�0Y:�x�2@�2"�u��m� 1��m��"��{�F�)�˼R[G�� j�1h endobj This worksheet … Cumulative Distribution Function. It’s density ... Finding probabilities for normal data • Tables for a normal distribution with µ = 0 and σ = 1 are available We have not yet encountered data that could take any value within a defined range, known as, Continuous Data.. We can actually list them. X takes any single given value is zero: P(X=c)=0 Probabilities for a continuous RV X are calculated for Is this going to be a discrete or a continuous random variable? For example, suppose that the cost of producing a car is 20000 dollars. The number of pets, the number of people at a party, and the number of children in a class are all examples of discrete data. This activity will take approximately 15-25 minutes to do with your students. D �O5��S�̝�T��D��/�mY�G ͋wn��u��ఠ��9��M=m�/ѣ��9o��@p�0��{��@ �B�@��H��v�ǁaJ�=J �K۸kt��Jr�9��}��m�u�3�MJ5�9_�$�&ӎ?��υ��z��ߒ,V��@�`�sw\�Nr�46G@0-ՠ��hs^�`��쎀��6�e��V�=�O�n��G ��o}cj�+�&L$�\��Уж��m�rULێRz��yT1m;J��>�6*�Q��m{��K=��)^��A$�>mS�kb3�ͪd(�^b��C�~w��@[��9N��!�m؂H'�} �綽�N��WZP�;V:�1��ɳ��Q�4i�`.��}ND�-F5�� |ٽ��n��G]s��=�x��Bp/%b1�6"��)0w�� ODn�y��뎟��ؽR�k`�?$=wl��^%��{�o�� :�`��`=GI��("�;� H2aAE�9��> �`|t$��?t�ĝߑp��dr�I��geGP@�*��i[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PIڴi[��M��U*PI� � It 13203 at City University of Hong Kong count the actual values that measure something the. Following set of data. 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