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It looks like you've uploaded a worksheet titled "Mean Absolute Deviation" that includes two data sets (Team A and Team B), with calculations for mean, absolute deviations, and the final Mean Absolute Deviation (MAD) values.

Let’s go through the problem step by step and verify or solve it correctly.

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🔹 Understanding Mean Absolute Deviation (MAD)

The Mean Absolute Deviation is a measure of variability that tells us how far, on average, each data point is from the mean.

#### Formula:
$$
\text{MAD} = \frac{\sum |x_i - \bar{x}|}{n}
$$
Where:
- $ x_i $ = each data value
- $ \bar{x} $ = mean of the data set
- $ n $ = number of data points

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## ✔ Step-by-step Solution:

We'll analyze both teams: Team A and Team B

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🟦 Team A

Data: 2, 15, 18, 4, 10
(From the table)

#### Step 1: Find the Mean ($\bar{x}$)
$$
\bar{x} = \frac{2 + 15 + 18 + 4 + 10}{5} = \frac{49}{5} = 9.8
$$

But in your table, the mean is written as 9.8, which matches.

#### Step 2: Find Absolute Deviations from the Mean

| Data | $ x_i - \bar{x} $ | $ |x_i - \bar{x}| $ |
|------|---------------------|-----------------------|
| 2 | 2 - 9.8 = -7.8 | 7.8 |
| 15 | 15 - 9.8 = 5.2 | 5.2 |
| 18 | 18 - 9.8 = 8.2 | 8.2 |
| 4 | 4 - 9.8 = -5.8 | 5.8 |
| 10 | 10 - 9.8 = 0.2 | 0.2 |

Sum of absolute deviations:
$$
7.8 + 5.2 + 8.2 + 5.8 + 0.2 = 27.2
$$

#### Step 3: Calculate MAD
$$
\text{MAD}_A = \frac{27.2}{5} = 5.44
$$

✔ Your table shows 5.44 — this is correct!

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🟨 Team B

Data: 7, 22, 11, 18, 26, 22, 15, 13, 21, 22
(From the table)

#### Step 1: Find the Mean

Add all values:
$$
7 + 22 + 11 + 18 + 26 + 22 + 15 + 13 + 21 + 22 = 175
$$

Number of data points: $ n = 10 $

$$
\bar{x} = \frac{175}{10} = 17.5
$$

✔ Your table says 17.5 — correct.

#### Step 2: Absolute Deviations

| Data | $ x_i - \bar{x} $ | $ |x_i - \bar{x}| $ |
|------|---------------------|-----------------------|
| 7 | 7 - 17.5 = -10.5 | 10.5 |
| 22 | 22 - 17.5 = 4.5 | 4.5 |
| 11 | 11 - 17.5 = -6.5 | 6.5 |
| 18 | 18 - 17.5 = 0.5 | 0.5 |
| 26 | 26 - 17.5 = 8.5 | 8.5 |
| 22 | 22 - 17.5 = 4.5 | 4.5 |
| 15 | 15 - 17.5 = -2.5 | 2.5 |
| 13 | 13 - 17.5 = -4.5 | 4.5 |
| 21 | 21 - 17.5 = 3.5 | 3.5 |
| 22 | 22 - 17.5 = 4.5 | 4.5 |

Sum of absolute deviations:
$$
10.5 + 4.5 + 6.5 + 0.5 + 8.5 + 4.5 + 2.5 + 4.5 + 3.5 + 4.5 = 50.0
$$

#### Step 3: Calculate MAD
$$
\text{MAD}_B = \frac{50.0}{10} = 5.0
$$

✔ Your table shows 5.0 — correct.

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📊 Final Comparison

- Team A MAD: 5.44
- Team B MAD: 5.0

So, Team B has less variability (smaller MAD).

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❓ Question at the Bottom:

> "Which team has more consistent performance? Explain."

✔ Answer:
Team B has more consistent performance because its Mean Absolute Deviation (5.0) is smaller than Team A's (5.44). This means the scores in Team B are, on average, closer to the mean than those in Team A.

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✔ Summary

| Team | Mean | MAD | Consistency |
|------|------|-----|-------------|
| A | 9.8 | 5.44 | Less consistent |
| B | 17.5 | 5.0 | More consistent |

✔️ All calculations in your worksheet are correct.

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