# Collecting and describing data

## Mathematics - Eighth Grade

### Collecting and describing data

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### Collecting and describing data

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### Collecting and describing data

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### Collecting and describing data

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#### Study Guide Collecting and describing data

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COLLECTING AND DESCRIBING DATA Collecting and describing data refers to the different ways to gather data and the different ways to arrange data whether it is in a table, graph, or pie chart. Data can be collected by either taking a sample of a population or by conducting a survey. Describing data looks at data after it has been organized and makes conclusions about the data. Many ideas in every day life can be put into a mathematical perspective. o Consider a sample of students in a class and their heights: this data can be collected and described by using a bar graph. Then from the bar graph, certain conclusions can be made regarding the measures of central tendency and the variability of the data. Measures of central tendency refer to the mean, mode and median of the data. Variability refers to the range, variance, interquartile range and standard deviation of the data. How to use collecting and describing data To collect and describe data, a sample of the population must be taken or a survey can be conducted. For example, a survey of the students in a class regarding the number of siblings is taken. The table shows the results. These results can be made into a bar graph. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
To describe this data, the measures of central tendency and variability are used. The mode for this data is 2, which means that most students have 2 siblings. The interquartile range is the range of the middle 50% of the data. This is found by finding the median of the data and then finding the median of first half of the data and the second half of the data, or the first quartile and the third quartile. The interquartile range for this data is 1, which means that the middle 50% of the data has a range of 1 and the data is very close together. Variance of the data also shows how close or spread out data can be. Data with a small variance means that the data is clustered. Data with a large variance means the data is spread out. The standard deviation is the square root of the variance. In a normal distribution, 68% of the data falls within one standard deviation of the mean. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Try This! 1. Based on the graph, what are the mean, mode and median of the data? 2. What is the range and interquartile range? 3. If the variation is 1.211, what is the standard deviation? 4. Based on the graph, how many people spend two hours on the computer? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.