Chapter 11/12 Notes The mean, median and mode are Measures of Center. The mean of a data set is the sum of the data divided by the number of pieces of data. The median of a list of values is the value appearing at the center of a sorted version of the list, or the mean of the two central values, if the list contains an even number of values. The mode is the number or numbers that occur most often. Find the mean, median, and mode of the data set, 22,13,11,16,14,13,16. mean: 22 + 13 + 11 + 16 + 14 + 13 + 16 7 = 105 7 or 15 To find the median, write the data in order from least to greatest. median: 11, 13, 13,14, 16, 16, 22 To find the mode, find the number or numbers that occur most often. mode: 11,13, 13, 14,16, 16, 22 The mean is $15. The median is $14. There are two modes, $13 and $16. Measures of Variation are used to describe the distribution, or spread, of the data. The range is the difference between the greatest and least data values. Quartiles are values that divide the data set into four equal parts. The median of the lower half of a set of data is the first quartile and the median of the upper half of a set of data is the third quartile. The difference between the third quartile and the first quartile is called the interquartile range. Find the measures of variation for the number of votes received for student government president: 13, 20, 18, 12, 21, 2, 18, 17, 15, 10, and 14. The greatest number in the data set is 21. The least number is 2. The range is 21 – 2 or 19 votes. To find the quartiles, arrange the numbers in order from least to greatest. Q1 median Q3 2 10 12 13 14 15 17 18 18 20 21 The interquartile range is 18 – 12 or 6. The mean absolute deviation is a measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing the number of data values. Find the mean absolute deviation of the set of data. Describe what the mean absolute deviation represents. 3, 8, 11, 5, 9, 6, 10, 4 Find the mean. 3 + 8 + 11 + 5 + 9 + 6 + 10 + 4 8 =7 Find the absolute value of the differences between each value in the data set and the mean. Each data value is represented by an x. Find the average of the absolute values of the differences between each value in the data set and the mean. 4+3+2+1+1+2+3+4 = 2.5 8 The mean absolute deviation is 2.5. This means that the data values are an average distance of 2.5 hours from the mean. Data from a frequency table can be displayed as a histogram, a type of bar graph used to display numerical data that have been organized into equal intervals. These intervals show the frequency distribution of the data, or how many pieces of data are in each interval. A box plot is a diagram that is constructed using the median, quartiles, and extreme values. A box is drawn around the quartile values, and the whiskers extend from each quartile to the extreme values.