Mean Absolute Deviation - Free Printable

Let's solve the problem step by step to find the Mean Absolute Deviation (MAD).

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Step 1: Find the Mean of the Data

Given data points:
87, 94, 72, 65, 97, 77

Add them up:
$$
87 + 94 + 72 + 65 + 97 + 77 = 502
$$

Divide by the number of data points (6):
$$
\frac{502}{6} = 83.67 \quad \text{(Wait! The image says 82, but let's check)}
$$

But in the image, it says:
$$
\frac{87+94+72+65+97+77}{6} = 82
$$

Let’s verify:
$$
87 + 94 = 181 \\
181 + 72 = 253 \\
253 + 65 = 318 \\
318 + 97 = 415 \\
415 + 77 = 492
$$

So total is 492, not 502.

$$
\frac{492}{6} = 82 \quad \text{✓ Correct}
$$

✔ So the mean is 82.

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Step 2: Subtract the Mean from Each Data Point and Take Absolute Values

We subtract 82 from each value and take the absolute value (remove negative signs):

1. $ |87 - 82| = |5| = 5 $
2. $ |94 - 82| = |12| = 12 $
3. $ |72 - 82| = |-10| = 10 $
4. $ |65 - 82| = |-17| = 17 $
5. $ |97 - 82| = |15| = 15 $
6. $ |77 - 82| = |-5| = 5 $

So the absolute deviations are:
$$
5, 12, 10, 17, 15, 5
$$

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Step 3: Find the Mean of These Absolute Deviations

Add them:
$$
5 + 12 = 17 \\
17 + 10 = 27 \\
27 + 17 = 44 \\
44 + 15 = 59 \\
59 + 5 = 64
$$

Now divide by 6:
$$
\frac{64}{6} \approx 10.67
$$

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✔ Final Answer:

Mean Absolute Deviation (MAD) ≈ 10.67

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Summary of Steps:

| Step | Description |
|------|-------------|
| 1 | Mean = $ \frac{87+94+72+65+97+77}{6} = 82 $ |
| 2 | Absolute deviations: 5, 12, 10, 17, 15, 5 |
| 3 | MAD = $ \frac{5+12+10+17+15+5}{6} = \frac{64}{6} \approx 10.67 $ |

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✔ Answer: The Mean Absolute Deviation is approximately 10.67.