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Topic: Mean Absolute Deviation

Topic: Mean Absolute Deviation Common Core/Essential Standards: 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

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Topic: Mean Absolute Deviation

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  1. Topic: Mean Absolute Deviation Common Core/Essential Standards:6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.5 Summarize numerical data sets in relation to their context, such as by: c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. 7.SP.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 distributions of heights is noticeable. MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically.

  2. There are two ways to describe a set of data… • Graphically • Numerically

  3. Measures of Spread describe how much values typically vary from the center These measures are: • Range “typical”: highest data point – lowest data point • Interquartile Range (IQR) : the middle 50% of the data ; found using Q3 – Q1 • Mean Absolute Deviation: how much data values vary from the mean. *A low MAD indicates that the data points are close to the mean and are not spread out, a high MAD, points are spread out*

  4. Thinking about the Situation Consider the following test scores: Who is the best student? How do you know? Take a few minutes to decide.

  5. The MEAN ABSOLUTE DEVIAITON (MAD) will help us understand the spread of our data. Let’s take a few minutes to explore MAD.

  6. Mean Absolute Deviation (MAD) Add to notes STEP 1: Find the mean STEP 2: Subtract the mean from each piece of data STEP 3: Find the absolute value of each difference STEP 4: Find the mean of the new differences (deviations) NOW WE WILL TRY THIS METHOD.

  7. Mean Absolute Deviation Write the list of numbers shown on the number line and then find the Mean Absolute Deviation 0 1 2 3 4 5 6 7 8 9 10 11 STOP AND COMPLETE CHART on NOTES

  8. So what exactly is deviation? -4 -3 +5 -1 +3 0 1 2 3 4 5 6 7 8 9 10 11 (-4) + (-3) + (-1) = -8 (+5 ) + (+3) = +8

  9. Mean Absolute Deviation -3.2 +3.2 0 1 2 3 4 5 6 7 8 9 10 11 Notice that our Mean Absolute Deviation or MAD was 3.2 and most of our original data does fall within plus or minus 3.2 points of the mean of 5.

  10. A low mean absolute deviation indicates that the data points tend to be very close to the mean making the data more consistent. A high mean absolute deviation indicates that the data points are spread out over a large range of values making the data less consistent.

  11. Now take a few minutes to go back to our original question about the best student. Find the MAD score for each student and then make a decision based on all of your data about the best student. Be prepared to discuss.

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