Review of Mean Median Mode and Mean Absolute

Review of Mean, Median, Mode, and Mean Absolute Deviation (MAD) Section 9. 4 in book

Measures of Central Tendency Mean: The sum of the data divided by the number of items in the data set. - Most useful when the data has no extreme values Median: The middle number of the data ordered from least to greatest, or the mean of the middle two numbers. - Most useful when the data has extreme values and there are no big gaps in the middle of the data. Mode: The number or numbers that occur most often. - Most useful when the data has many identical numbers.

Example 1: Find the mean, median, and mode of the following data. 68, 79, 84, 93, 68, 82, 76, 90 Put the data in order from least to greatest. 68, 76, 79, 82, 84, 90, 93 Mean: (68 + 76 + 79 + 82 + 84 + 90 + 93) ÷ 8 = 80 Median: Since there is an even number of data values, find the mean of the two center values. (79 + 82) ÷ 2 = 80. 5 Mode: 68 is the mode because it is the value that occurs most often.

Mean Absolute Deviation: The average distance between each data value and the mean in a set of data. - Can be used to describe the distribution of a set of data Using the data set from Example 1, Data value Mean Distance from mean 68 68 76 79 82 84 90 93 80 80 12 12 4 10 13 Mean absolute deviation: (12 + 4 + 1 + 2 + 4 + 10 + 13) ÷ 8 = 7. 25 The mean absolute deviation is 7. 25. This means that the average distance between each data value and the mean is 7. 25.

Example 2: For each of the following data sets, find: Temperatures while camping (o. F) Daily lows Daily highs a) the mean, median, and mode. 55 73 54 75 b) the mean absolute deviation. 50 84 61 71 54 82 59 65 For the daily low temperatures, Mean: (50 + 54 + 55 + 59 + 61) ÷ 6 = 55. 5 o. F Median: (54 + 55) ÷ 2 = 54. 5 o. F Mode: 54 o. F is the value that occurs most often. For the daily high temperatures, Mean: (65 + 71 + 73 + 75 + 82 + 84) ÷ 6 = 75 o. F Median: (73 + 75) ÷ 2 = 74 o. F Mode: No data value repeats. There is no mode.

Example 2 b: Find the mean absolute deviation for each set. Daily lows (o. F) Mean of lows Distance from mean Daily highs (o. F) Mean of highs Distance from mean 50 55. 5 65 75 10 54 55. 5 1. 5 71 75 4 54 55. 5 1. 5 73 75 2 55 55. 5 0. 5 75 75 0 59 55. 5 3. 5 82 75 7 61 55. 5 84 75 9 Mean absolute deviation of low temps: Mean absolute deviation of high temps: (5. 5 + 1. 5 + 0. 5 + 3. 5 + 5. 5) ÷ 6 (10 + 4 + 2 + 0 + 7 + 9) ÷ 6 = 3 o. F ≈ 5. 3 o. F Since the mean absolute deviation of the daily low temperatures is less than that of the daily high temperatures, the daily low temperatures are closer together than the daily high temperatures.