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Summarizing Numerical Data Sets

This guide explores the key concepts of measures of center and variability, essential for analyzing numerical data sets. It explains the mean as the average value and the median as the middle-most value in a data set, highlighting their importance in generalizing data. The interquartile range and mean absolute deviation are introduced as measures of variability. These tools help describe the spread of data and identify common values, allowing for deeper insights into data sets. A practical example illustrates calculating the mean absolute deviation for a set of orders.

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Summarizing Numerical Data Sets

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  1. Summarizing Numerical Data Sets ~ adapted from Walch Education

  2. Measures of Center • The mean and median are two measures of center. • The mean is the average value of the data. • The median is the middle-most value in a data set. • These measures are used to generalize data sets and identify common or expected values.

  3. Measures of Center, continued… The mean is useful when data sets do not contain values that vary greatly.

  4. Measures of Variability • Interquartile range and mean absolutedeviation describe variability of the data set. • Interquartile range is the difference between the third and first quartiles. • The first quartile is the median of the lower half of the data set. • The third quartile is the median of the upper half of the data set.

  5. Measures of Variability, continued… • The mean absolute deviation is the average absolute value of the difference between each data point and the mean. • Measures of spread describe the variance of data values (how spread out they are), and identify the diversity of values in a data set. • Measures of spread are used to help explain whether data values are very similar or very different.

  6. Measures of Variability, continued… • The mean absolute deviation takes the average distance of the data points from the mean.

  7. Measures of Variability, continued… The interquartile range finds the distance between the two data values that represent the middle 50% of the data.

  8. Let’s Try a Problem! A website captures information about each customer’s order. The total dollar amounts of the last 8 orders are listed in the table to the right. What is the mean absolute deviation of the data?

  9. To find the mean absolute deviation of the data, start by finding the mean of the data set. NEXT STEP….Find the absolute value of the difference between each data value and the mean: |data value – mean|

  10. Here we go… |21 – 21| = 0 |15 – 21| = 6 |22 – 21| = 1 |26 – 21| = 5 |24 – 21| = 3 |21 – 21| = 0 |17 – 21| = 4 |22 – 21| = 1 Find the sum of the absolute values of the differences. 0 + 6 + 1 + 5 + 3 + 0 + 4 + 1 = 20

  11. Divide the sum of the absolute values of the differences by the number of data values. THE MEAN ABSOLUTE DEVIATION OF THE DOLLAR AMOUNTS OF EACH ORDER SET IS 2.5. THIS SAYS THAT THE AVERAGE COST DIFFERENCE BETWEEN THE ORDERS AND THE MEAN ORDER IS $2.50

  12. Thanks for Watching!!!!! ~Ms. Dambreville

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