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

Options

A. 5.2
B. 0.5
C. 0.6
D. 0.7

Answer

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
First, we need to calculate the mean (average) of the given numbers.

\[ \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}} \]

The numbers are 10, 9, 21, 16, and 24.

Calculating the sum:

\[ 10 + 9 + 21 + 16 + 24 = 80 \]

Now, divide by the total number of values (which is 5):

\[ \text{Mean} = \frac{80}{5} = 16 \]

### Step 2: Calculate the Deviations from the Mean
Next, we will find the absolute deviations of each number from the mean.

\[ \text{Deviations} = |X_i - \text{Mean}| \]

Calculating each deviation:

- 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 the Deviations
Now, we will sum all the absolute deviations we calculated:

\[ \text{Sum of Deviations} = 6 + 7 + 5 + 0 + 8 = 26 \]

### Step 4: Calculate the Mean Deviation
Finally, we will calculate the mean deviation by dividing the sum of deviations by the total number of values.

\[ \text{Mean Deviation} = \frac{\text{Sum of Deviations}}{\text{Total number of values}} = \frac{26}{5} = 5.2 \]

### Conclusion
Thus, the mean deviation from the mean of the numbers 10, 9, 21, 16, and 24 is **5.2**.

---