Simplify the expression below: (-5x² + 2) - (4x² – 5x - 9)
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Answer: See the diagram below
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Explanation:
She starts off finding the mean of the data. So she adds up the values to get 48+54+57+62+69 = 290, and then divides by 5 to get the mean of 290/5 = 58. That explains why there's a 58 in the first row of the second column.
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For the next step, she subtracts 58 from each data item. If the result is negative, then go with the positive version (ie apply the absolute value)
- |48-58| = 10
- |54-58| = 4
- |57-58| = 1
- |62-58| = 4
- |69-58| = 11
This leads to the list 10,4,1,4,11 which goes in the first slot labeled "drag and drop an item here". This is the list of distance values each item is from the mean.
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The last thing to do is find the mean of the set {10,4,1,4,11}
add: 10+4+1+4+11 = 30
divide by five: 30/5 = 6
The mean absolute deviation (MAD) is 6
This represents the average distance each data value is from the mean. The MAD tells us how spread out the data is. It's similar to the standard deviation.
