Answer: 2
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Step-by-step explanation:
Each purple symbol on the pictograph refers to 2 wands.
- Glenda has 2 such symbols, so she has 2*2 = 4 wands
- Tink has 3 symbols to lead to 2*3 = 6 wands
- Merry has 4 symbols to lead to 2*4 = 8 wands
- Gracie has 5 symbols which means 2*5 = 10 wands
The wand counts from left to right are: 4, 6, 8, 10
Add them up and divide by four to get the arithmetic mean
(4+6+8+10)/4 = 28/4 = 7
The mean is 7. If we distributed the number of wands (28) equally among the four women, then each would get 7.
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Now subtract each data value from the mean. Apply absolute value to ensure the difference or distance is not negative. This is what the "absolute" refers to in "mean absolute deviation".
- |4-7| = 3
- |6-7| = 1
- |8-7| = 1
- |10-7| = 3
The absolute deviations from the mean is the list of: 3, 1, 1, 3
This is the list of distances from the mean.
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The last step is to compute the mean of the set {3,1,1,3}
Add: 3+1+1+3 = 8
Divide by four: 8/4 = 2
The mean absolute deviation (MAD) is 2
This is the average distance each data value from {4,6,8,10} is from the mean of 7. It might help to draw out a number line to see this.