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High School Graduation Test Review Domain: Data Analysis How is data presented, compared and used to predict future outcomes?

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The standards for this domain… MM1D1 Students will determine the number of outcomes related to a given event. MM1D2 Students will use the basic laws of probability. MM1D3 Students will relate samples to a population. MM2D1 Using sample data, students will make informal inferences about population means and standard deviations. MM2D2 Students will determine an algebraic model to quantify the association between two quantitative variables.

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MM1D3 STUDENTS WILL RELATE SAMPLES TO A POPULATION.

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SAMPLES– MM1D3 Summary Statistics Population vs Sample Representative Sample -- Random

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Summary Statistics Mean 5 number summary (Box & Whisker Plot) Range

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Mean Average

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5 NUMBER SUMMARY – BOX & WHISKER PLOT

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Range How far from the lowest value to the highest value (subtract)

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Now you try one… Linda's first five Math II tests scores were 75, 82, 74, 95, and 89. If her mean semester average was 85, what score did she make on her sixth and last test? 95

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Which would be better median or mean? If each of the 20 random samples collected contains several outliers, which of the following will give the best estimate of where the center of the actual population lies? Median because it is more resistant to outliers.

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Population vs Sample Sample is the PART of the population that you survey for your study. The key is selecting a representative sample.

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Representative Sample The sample must be Random! The larger the sample the closer to the population. If a small sample, the more samples the closer to the population.

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Example A population was sampled ten times. The medians of the samples are: 17, 17, 17, 18, 19, 19, 20, 20, 21, 21 Can we use these sample medians to predict the median of the population?

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Example answer YES – take the mean of the sample medians which would be 18.9 So a good estimate of the median of the actual population would be 19.

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Representative Sample Random is always representative.

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Sample Types Self selected – volunteer Systematic – rule or pattern Convenience – easy to contact Biased – skewed – not representative Unbiased – representative of the population

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Example… Janet is surveying students at her school. Which of the following would most likely give her a representative sample? a. Surveying only her homeroom b. Surveying the first 60 students who walk up to her at lunch c. Surveying only the members of the school chorus d. Surveying 50 students from each grade who have been randomly selected by a computer. D – why?

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WHY? what type of sample… What type of samples are these and what is wrong with them? a. Surveying only her homeroom -- convenience b. Surveying the first 60 students who walk up to her at lunch-- volunteer c. Surveying only the members of the school chorus -- biased d. Surveying 50 students from each grade who have been randomly selected by a computer. -- systematic

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Now you try one… A principal is surveying the parents of his students to find out if they would support extending the school day by 20 minutes. Which method would most likely result in a representative sample? a. Surveying every 20th name from a list of all school parents b. Surveying 50 parents of ninth graders. c. Surveying parents that attend the monthly PTO meeting d. Surveying parents who volunteer in the media center. A

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The mean is typically what is meant by the word “average.” The mean is perhaps the most common measure of central tendency. The sample mean is written.

The mean is typically what is meant by the word “average.” The mean is perhaps the most common measure of central tendency. The sample mean is written.

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