of interest. Generate multiple Use proportional reasoning to make estimates relating to a population on samples (or simulated samples) the basis of a sample. of the same size to gauge the Inferences a population are only valid if the sample is random and variation in estimates or representative. predictions. For example, Having multiple samples for the same population allows for gauging the estimate the mean word length variation of estimates or predictions. in a book by randomly sampling words from the book; predict the winner of a school election based Examples: on randomly sampled survey Below is the data collected from two random samples of 100 students data. Gauge how far off the regarding student’s school lunch preferences. Make at least two inferences estimate or prediction might be. based on the results. (S) Source: Arizona Academic Content Standards Illustrative Mathematics Task: 7.SP.B.3. Informally assess the Notes: Background Information: degree of visual overlap of two This is the students’ experience with comparing two data sets. Students numerical data distributions build on their understanding of graphs, mean, median, Mean Absolute with similar variabilities, Deviation (M.A.D.) and interquartile range from 6th grade. Mean absolute measuring the difference deviation is an element of a data set that is the absolute difference between between the centers by that element and a given point. Lesson expressing it as a multiple of a Measures of center can be used to compare data and measure variability measure of variability. For between data sets. Use the mean (or other measures of center) to find the example, the mean height of difference between the centers as a measure of variability. players on the basketball team is Data displays are used to visually compare data sets and draw informal 10 cm greater than the mean comparative inferences. Box plots are way to show measures of variability Mean Absolute Deviation height of players on the soccer such as the range (Other data displays may highlight other measures of (Glencoe Lesson Seed) team, about twice the variability variability). Use observations to about mean differences between two or more samples (mean absolute deviation) on either team; on a dot plot, the to make conjectures about the populations from which the samples were Illustrative Mathematics separation between the two taken. Task:
of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. (S) Use proportional reasoning to make estimates relating to a population on the basis of a sample. Inferences a population are only valid if the sample is random and representative. Having multiple samples for the same population allows for gauging the variation of estimates or predictions. Examples: Below is the data collected from two random samples of 100 students regarding student’s school lunch preferences. Make at least two inferences based on the results. Source: Arizona Academic Content Standards Illustrative Mathematics Task: 7.SP.B.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two Notes: This is the students’ experience with comparing two data sets. Students build on their understanding of graphs, mean, median, Mean Absolute Deviation (M.A.D.) and interquartile range from 6th grade. Mean absolute deviation is an element of a data set that is the absolute difference between that element and a given point. Measures of center can be used to compare data and measure variability between data sets. Use the mean (or other measures of center) to find the difference between the centers as a measure of variability. Data displays are used to visually compare data sets and draw informal comparative inferences. Box plots are way to show measures of variability such as the range (Other data displays may highlight other measures of variability). Use observations to about mean differences between two or more samples to make conjectures about the populations from which the samples were taken. Background Information: Lesson Mean Absolute Deviation (Glencoe Lesson Seed) Illustrative Mathematics Task:
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