To compute the Mean Absolute Deviation (MAD), we proceed step by step:

1. Step 1: Find the mean of the data set.
   The data set is: $126, 138, 276, 178, 236, 90$.
   The formula for the mean is:
   $\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$

   $\text{Mean} = \frac{126 + 138 + 276 + 178 + 236 + 90}{6} = \frac{1044}{6} = 174$

2. Step 2: Calculate the absolute deviations for each data value.
   The formula for absolute deviation is:
   $\text{Absolute Deviation} = \lvert \text{Data Value} - \text{Mean} \rvert$

   Compute for each value:

   • For $126$:
     $\lvert 126 - 174 \rvert = 48$
   • For $138$:
     $\lvert 138 - 174 \rvert = 36$
   • For $276$:
     $\lvert 276 - 174 \rvert = 102$
   • For $178$:
     $\lvert 178 - 174 \rvert = 4$
   • For $236$:
     $\lvert 236 - 174 \rvert = 62$
   • For $90$:
     $\lvert 90 - 174 \rvert = 84$

3. Step 3: Compute the MAD.
   The formula for MAD is:
   $\text{MAD} = \frac{\text{Sum of absolute deviations}}{\text{Number of values}}$

   Sum of absolute deviations:
   $48 + 36 + 102 + 4 + 62 + 84 = 336$

   MAD:
   $\text{MAD} = \frac{336}{6} = 56$

Final Table:

Data Value	Absolute Deviation
126	$48$
138	$36$
276	$102$
178	$4$
236	$62$
90	$84$

MAD = 56

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Let me know if you'd like a deeper explanation!
Here are five follow-up questions for practice:

1. What is the significance of the MAD in analyzing data?
2. How does increasing or decreasing one value in the data set affect the MAD?
3. Can you calculate the MAD for a new data set, $200, 210, 220, 230, 240$?
4. What is the relationship between the MAD and variance?
5. Why do we use absolute values instead of regular differences in MAD calculation?

Tip: The MAD is a great measure of variability, especially when dealing with data sets that may contain outliers!