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These advances have ensured that after the collection and analysis of large datasets, the results can be distributed very quickly. It is very important that future planning and decisions are based on current empirical data as change is fast-paced and costly in the modern world. In 1880 a census was conducted in the USA and it took 7 years for the information collected by the census to be published. The very  \ndetailed dataset collected by the Australian census in August 2016 was released in June 2017 .  \nData has the power to initiate change and business and governments ignore it at their peril. Meteorologists, urban planners, health scientists, traffic engineers, pharmaceutical companies, environmental scientists, educators and agriculturalists to name a few, use data to monitor change and make future predictions. These changes may be as small as choosing to block off a suburban street to stop too many people using it as a short cut and creating traffic problems, or as big as ensuring that there is enough food production to feed anever-increasing world population. Decisions that require major societal change, practice and investment need to be justified. Empirical evidence can provide this justification and therefore it is important that everyone has some knowledge and understanding of the collection and interpretation of data.  \nLEARNING SEQUENCE  \n1.1 Overview  \n1.2 Types of data  \n1.3 Stem plots  \n1.4 Dot plots, frequency tables and histograms, and bar charts  \n1.5 Describing the shape of stem plots and histograms  \n1.6 The median, the interquartile range, the range and the mode  \n1.7 Boxplots  \n1.8 The mean of a sample  \n1.9 Standard deviation of a sample  \n1.10 Populations and simple random samples  \n1.11 The 68–95–99 .7% rule and z-scores  \n1.12 Review: exam practice  \nFully worked solutions for this topic are available in the Resources section of your eBookPLUS at [www.jacplus.com.au](www.jacplus.com.au).  \nTOPIC 1 Investigating data distributions 1  \n~~i~~  \n~~i ~~  \n“c01InvestigatingDataDistributions_print” — 2018/9/12 — 7:52 — page 2 — \\#2  \n~~i~~  \n~~ i~~  \n1.1.2 Kick off with CAS  \nExploring histograms with CAS  \nHistograms can be used to display numerical data sets. They show the shape and distribution of a data set, and can be used to gather information about the data set, such as the range of the data set and the value of the median (middle) data point.  \n1. The following data set details the age of all of the guests at a wedding.  \n\n| Age | Frequency |\n| --- | --- |\n| 0– | 4 |\n| 10– | 6 |\n| 20– | 18 |\n| 30– | 27 |\n| 40– | 14 |\n| 50– | 12 |\n| 60– | 6 |\n| 70– | 3 |\n| 80– | 2 |\n\nUse CAS to draw a histogram displaying this data set.  \n2. Comment on the shape of the histogram. What does this tell you about the distribution of this data set?  \n3. a. Use CAS to display the mean of the data set on your histogram.  \nb. What is the value of the mean?  \n4. a. Use CAS to display the median of the data set on your histogram.  \nb. What is the value of the median?  \nPlease refer to the Resources section in the Prelims of your eBookPLUS for a comprehensive step-by-step guide on how to use your CAS technology.  \n2 Jacaranda Maths Quest 12 Further Mathematics VCE Units 3 & 4 Sixth Edition  \n~~i~~  \n~~i ~~  \n“c01InvestigatingDataDistributions_print” — 2018/9/12 — 7:52 — page 3 — \\#3  \n~~i~~  \n~~ i~~  \n1.2 Types of data  \nUnivariate data are data that contain one variable. That is, the information deals with only one quantity that changes. Therefore, the number of cars sold by a car salesman during one week is an example of univariate data. Sets of data that contain two variables are called bivariate data an","cbCainOAWj9HJ48r","https://ap.wps.com/l/cbCainOAWj9HJ48r","pdf",7808661,98,"English","# TOPIC 1 Investigating data distributions\n## 1.1 Overview\n## 1.2 Types of data\n## 1.2.1 Types of data\n## 1.2.2 Discrete and continuous data\n## Worked example 1","[{\"question\":\"Why are data collection and analysis important for planning and decisions?\",\"answer\":\"Because results from large datasets can be distributed quickly, enabling future planning to be based on current empirical evidence. It helps justify changes that are fast-paced and costly.\"},{\"question\":\"How does a histogram help in studying a data set?\",\"answer\":\"A histogram displays numerical data sets and reveals their shape and distribution. It supports finding information such as the range and the median value.\"},{\"question\":\"What is the difference between discrete and continuous data?\",\"answer\":\"Discrete data take fixed values that can be counted, such as the number of children per household. Continuous data can take any value within a range, such as measured temperatures or student heights.\"}]","Investigating data distributions - Topic 1 - Overview | PDF",247]