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1.5.3. Mean Absolute Deviation
The Mean Absolute Deviation (MAD) of a dataset is the average distance between each data value and the mean. It
helps us get a sense of how "spread out" the values in a dataset are. MAD is the average of how far away all values
in a dataset are from the mean. Let us understand this with an example.
Example 1.7: The scores on a science test are shown below.
86, 93, 88, 85, 89, 95, 85, 83
Find and interpret the mean absolute deviation of the data.
Step 1 Mean = 86 + 93 + 88 + 85 + 89 + 95 + 85 + 83 = 704/ 8 = 88
Step 2 Calculate the distance of each data point from the mean. (As given in third column in following table). You
need to find the absolute value after removing plus or minus as given in the fourth column.
Data Point Mean Distance from mean Absolute value
86 88 -2 2
93 88 5 5
88 88 0 0
85 88 -3 3
89 88 1 1
95 88 7 7
85 88 -3 3
83 88 -5 5
Sum of absolute Values = Sum 26
Mean absolute Deviation = Sum/n 3.25
Step 3 Calculate the sum of this column (= 26) and divide it by the numbers of data points, i.e., 8. The Mean
26
Absolute Deviation shall be mean of this sum = = 3.25.
8
The value of MAD gives a very good understanding of the variability of the dataset or in other words how scattered
the dataset is?
The "range" of a list of numbers is just the difference between the largest and smallest values.
Activity 3
1. Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13
2. Find and interpret the mean absolute deviation of the data.
(a) 9, 10, 11, 11, 12, 12, 13, 13, 14, 15
(b) 2, 4, 4, 5, 6, 7, 7, 7
(c) 24, 26, 27, 27, 28, 28, 30, 32 4. 8, 28, 29, 31, 32, 35, 38, 41, 43
1.5.4. Mode
The mode means the number that appears the most in a dataset. A set of numbers may have one mode, or more
than one mode, or no mode at all. Let us take an example.
Example 1.8: Find the mode of the following set of scores {14 11 15 9 11 15 11 7 13 12}.
Here the mode is 11 because 11 occurred more times than the other numbers. Sometimes there may not be any
mode value as there may not be any repetition of data values.
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