Mean, Median, Mode, Range, Outlier, & Mean Deviation Statistics Mean, Median, Mode, Range, Outlier, & Mean Deviation

Mean Mean (Average): the sum of the numbers divide by the amount of numbers. Ex: What is the average of the following numbers: 3, 4, 3, 3, 4, 5, 1, and 1? 3+4+3+3+4+5+1+1 8 = 24 8 = 3

Median Median (Middle): arrange the numbers in order and find the middle number; if there are two numbers in the middle, find their mean (average) Ex: What is the median of the following numbers: 3, 4, 3, 3, 4, 5, 1, and 1? 1, 1, 3, 3, 3, 4, 4, 5 Median = 3+3 2 = 3 Ex: What is the median of the following numbers: 3, 4, 3, 3, 4, 5, 1, 6, and 1? 1, 1, 3, 3, 3, 4, 4, 5, 6 Median = 3

Mode Mode (Most): arrange the numbers in order and find the number that occurs the most; their doesn’t have to be an answer, or there could be more than one. Ex: What is the mode of the following numbers: 3, 4, 3, 3, 4, 5, 1, and 1? 1, 1, 3, 3, 3, 4, 4, 5 Mode = 3 Ex: What is the mode of the following numbers: 1, 2, 2, 3, 2, 2, 3, 1, 3, 4, 3, 1? 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4 Mode = 2 & 3 Ex: What is the mode of the following numbers: 1, 3, 2, 4, 6, 5, 9, 7, 8, 0? 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Mode = ∅ (no mode)

Range Range (Distance): the distance between the biggest and smallest number; big – small = range. Ex: What is the range of the following numbers: 3, 4, 3, 3, 4, 5, 1, and 1? 1, 1, 3, 3, 3, 4, 4, 5 Range = 5 – 1 = 4

Outlier Outlier: a number that is outside; doesn’t belong with the group of numbers; there doesn’t have to be one, or there could be more than one. Ex: What is the outlier of the following numbers: 3, 4, -8, 3, 4, 5, 1, 10, 11, and 1? -8, 1, 1, 3, 3, 4, 4, 5, 10, 11 Outlier: -8, 10, & 11 Ex: What is the outlier of the following numbers: 3, 4, 3, 3, 4, 5, 1, and 1? 1, 1, 3, 3, 3, 4, 4, 5 No outlier

Mean Deviation Mean Deviation: the average (mean) of how far each number is from the actual average (mean); first, arrange all the numbers in order from least to greatest…then find the mean. Ex: What is the average of the following numbers: 3, 4, 3, 3, 4, 5, 1, and 1? 3+4+3+3+4+5+1+1 8 = 24 8 = 3 Now, find the average of how far each number is from the mean (which, in this case, is 3). 3 – 1 = 2 3 – 1 = 2 3 – 3 = 0 3 – 3 = 0 3 – 3 = 0 4 – 3 = 1 4 – 3 = 1 5 – 3 = 2 0+0+0+1+1+2+2+2 8 = 8 8 = 1 (this is the mean deviation).

Practice Define the mean, median, mode, range, outlier, and mean deviation of the following number sequences. 1. 0, 1, 2, 3, 9, 9, 7, 2, 3, 4, 4, 5, 6 2. 2, 0, 9, 4, 2, 1, 3, 0, 4, 9, 7, 8, 5 3. 0, 9, 7, 3, 2, 1, 4, 5, 7, 2 4. 0, 9, 2, 1, 7, 3, 4, 5, 0, 9, 7, 1, 23, 4, 5 5. 12, 3, 0, 9, 8, 4, 71, 23, 4, 8, 9, 7