What is the mean deviation from the mean of the numbers 10, 9, 21, 16, 24?

Options

A. `5.2`
B. `5.0`
C. `4.5`
D. `4.0`

Explanation

To find the mean deviation from the mean of the numbers 10, 9, 21, 16, and 24, we will follow these steps:

### Step 1: Calculate the Mean
The mean (average) is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]

First, we find the sum of the numbers:
\[ 10 + 9 + 21 + 16 + 24 = 80 \]

Next, we divide by the number of observations, which is 5:
\[ \text{Mean} = \frac{80}{5} = 16 \]

### Step 2: Calculate the Deviations from the Mean
Now we will find the absolute deviations of each number from the mean (16):
- For 10:
\[ |10 - 16| = | -6 | = 6 \]
- For 9:
\[ |9 - 16| = | -7 | = 7 \]
- For 21:
\[ |21 - 16| = |5| = 5 \]
- For 16:
\[ |16 - 16| = |0| = 0 \]
- For 24:
\[ |24 - 16| = |8| = 8 \]

### Step 3: Sum of Absolute Deviations
Now, we sum all the absolute deviations:
\[ 6 + 7 + 5 + 0 + 8 = 26 \]

### Step 4: Calculate the Mean Deviation
Finally, we calculate the mean deviation using the formula:
\[ \text{Mean Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Number of observations}} \]
\[ \text{Mean Deviation} = \frac{26}{5} = 5.2 \]

### Final Answer
The mean deviation from the mean of the numbers 10, 9, 21, 16, and 24 is **5.2**.

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