Find the standard deviation of {11, 7, 10, 13, 9}
A. 1
B. 2
C. 4
D. 5

Options

A. B
B. D
C. C
D. A

Answer

To find the standard deviation of the data set {11, 7, 10, 13, 9}, we will follow these steps:

### Step 1: Calculate the Mean (m)
The mean is calculated using the formula:

\[ m = \frac{\sum x_i}{n} \]

Where \(x_i\) are the data points and \(n\) is the number of data points.

For our data set:

\[ m = \frac{11 + 7 + 10 + 13 + 9}{5} = \frac{60}{5} = 12 \]

### Step 2: Calculate Each Deviation from the Mean
Now we will calculate the deviation of each data point from the mean:

- \(x_1 - m = 11 - 10 = 1\)
- \(x_2 - m = 7 - 10 = -3\)
- \(x_3 - m = 10 - 10 = 0\)
- \(x_4 - m = 13 - 10 = 3\)
- \(x_5 - m = 9 - 10 = -1\)

### Step 3: Square Each Deviation
Next, we square each of the deviations calculated in the previous step:

- \((1)^2 = 1\)
- \((-3)^2 = 9\)
- \((0)^2 = 0\)
- \((3)^2 = 9\)
- \((-1)^2 = 1\)

### Step 4: Calculate the Mean of the Squared Deviations
Now, we will find the mean of these squared deviations:

\[ \text{Mean of squared deviations} = \frac{1 + 9 + 0 + 9 + 1}{5} = \frac{20}{5} = 4 \]

### Step 5: Calculate the Standard Deviation
Finally, we take the square root of the mean of the squared deviations to find the standard deviation:

\[ SD = \sqrt{4} = 2 \]

Thus, the standard deviation of the data set {11, 7, 10, 13, 9} is **2**.

### Answer:
**B. 2**

---