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Five-number summaries  \n2. Outliers  \n3. Boxplots  \nVCAA key knowledge point:  \n“the five-number summary and the boxplot as its graphical representation and display, including the use of the lower fence (Q1 − 1.5 × IQR) and upper fence (Q3 + 1.5 × IQR) to identify possible outliers”  \nMathematics Area of Study key knowledge points derived from VCE Mathematics Study Design 2016-2020 p.22;© The Victorian Curriculum and Assessment Authority (VCAA). Used with permission.  \nLESSON YOU WILL FIND:  \n1. Five-number summaries  \nThe five-number summary is five values that give key information about a set of data and its distribution. The summary is as follows:  \n● Minimum value  \n● First quartile (Q1)  \n● Median (Q2)  \n● Third quartile (Q3)  \n● Maximum value.  \nExample  \n1  \nMinimum  \n2  \nQ1  \n3  \n4  \n5  \n6  \nMedian  \n7  \nQ3  \n8  \n9  \n10  \nMaximum  \nThe five-number summary for the data set 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is:  \n● Minimum: 1  \n● First quartile: 3  \n● Median: 5.5  \n● Third quartile: 8  \n● Maximum: 10  \nworked example 24 (1 mark)  \nCreate a five-number summary for the following data set:  \n18, 16, 21, 4, 24, 17, 34, 19, 15, 10, 14.  \nSolUTIoN  \nStep 1 Rewrite the data in ascending order:  \n4, 10, 14, 15, 16, 17, 18, 19, 21, 24, 34.  \nvalues.  \nStep 3 Find the position of the median (Q2) using the formula (1 ), where n is the number of elements in the data set.  \n11 + 1 = 6  \n2  \n4, 10, 14, 15, 16, 17, 18, 19, 21, 24, 34  \nThe median is the sixth element of the data set, which is 17.  \n© Edrolo 2018  \n17 2  \n18 The vertices represent shipping ports. The edges represent the paths ships can take.  \nThe ships cannot traverse all the paths without going over the same path twice.  \n19 D  \n20 C  \n21 B  \n Questions from multiple lessons   \n22 Network and decision mathematics Decoding the question  \nKeywords: sum, degrees, vertices  \nRelevant Lesson: 5A  \nWe must find the degree of each vertex in each graph, calculate the sum for each graph and then compare these values.  \nInformation we are given  \n• The given graphs  \nUsing the theory  \nThe degree of a vertex is equal to the number of edges connected to it.  \nThe degrees of each vertex can be found by counting the number of times an edge attaches to it. These are shown below.  \n3  \n4  \n2  2   \n2  \n2  3 3   3  \nGraph A Graph B  \nCalculate the sum of the degrees of the vertices for each graph.  \nGraph A: 2 + 2 + 2 + 3 + 3 = 12  \nGraph B: 3 + 3 + 2 + 4 = 12  \nCalculate the difference.  \n12 − 12 = 0  \n∴ The sum of the degrees of the vertices of Graph B is equal to the sum of the degrees of the vertices of graph A.  \nAnswer  \nC  \n1 mark – Correct answer  \n23 Data analysis Decoding the question  \nKeywords: boxplot, five-number summary  \nWe need to read features of the given boxplot to deduce the five-number summary of the data.  \nRelevant lesson: 12G  \nInformation we are given  \n• The given boxplot  \nUsing the theory  \nThe five-number summary’s location on the boxplot is shown below.  \nQ1  \nQ2  \n45 50 Median 60 65 70  \nLength (m)  \nHence, the five-number summary, reading from left to right, is: 41.2, 51.4, 54, 57.4, 72.  \nCareful! Outliers should be included in the  \nfive-number summary.  \nAnswer  \nA  \n1 mark – Correct answer  \n24a Networks and decision mathematics Decoding the question  \nKeywords: explain, adjacency matr","cbCaifvmuYRhOcg7","https://ap.wps.com/l/cbCaifvmuYRhOcg7","pdf",1265178,"English","# Introducing the Units 1& 2 Edrolo General Maths Textbooks - 2nd Edition\n## Boxplots and outliers\n## Questions from multiple lessons","[{\"question\":\"What is a five-number summary and what values does it include?\",\"answer\":\"A five-number summary consists of the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value. It describes the distribution and location of key points.\"},{\"question\":\"How are outliers identified using boxplots in this lesson?\",\"answer\":\"Outliers are identified using the lower fence (Q1 − 1.5 × IQR) and upper fence (Q3 + 1.5 × IQR). Values beyond these fences are treated as possible outliers.\"},{\"question\":\"How do calculators help find the five-number summary?\",\"answer\":\"The material provides step-by-step instructions to compute one-variable statistics and obtain the minimum, Q1, median, Q3, and maximum using TI-Nspire or Casio Classpad.\"}]","VCE General Mathematics - Units 1 & 2 - Boxplots and outliers | PDF",1789908631]