Question

Leah asked five of her friends how many sports they play. She received the following responses: 1, 1, 2, 3, and 3. Calculate the standard deviation of the data.(1 point)
The standard deviation is
Its not 0.8944

Answer 1

To calculate the standard deviation of Leah's friends' responses, we follow these steps:

1. **Find the mean (average)** of the data.
2. **Calculate the variance**.
3. **Take the square root of the variance** to get the standard deviation.

### Step 1: Calculate the Mean

The data points are: 1, 1, 2, 3, 3.

Mean (μ) = (Sum of all data points) / (Number of data points)

\[
\text{Mean} = \frac{1 + 1 + 2 + 3 + 3}{5} = \frac{10}{5} = 2
\]

### Step 2: Calculate the Variance

Variance (σ²) is calculated using the formula:

\[
\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}
\]

where \(x_i\) is each data point, μ is the mean, and N is the number of data points.

Now we calculate \((x_i - \mu)^2\) for each data point:

- For 1: \((1 - 2)^2 = (-1)^2 = 1\)
- For 1: \((1 - 2)^2 = (-1)^2 = 1\)
- For 2: \((2 - 2)^2 = (0)^2 = 0\)
- For 3: \((3 - 2)^2 = (1)^2 = 1\)
- For 3: \((3 - 2)^2 = (1)^2 = 1\)

Now, sum these squared differences:

\[
1 + 1 + 0 + 1 + 1 = 4
\]

Now, divide by the number of data points (N = 5):

\[
\sigma^2 = \frac{4}{5} = 0.8
\]

### Step 3: Calculate the Standard Deviation

Finally, take the square root of the variance:

\[
\sigma = \sqrt{0.8} \approx 0.8944
\]

However, it's important to note that if you are calculating the sample standard deviation (instead of population standard deviation), the denominator would be \(N - 1\) (which is 4):

\[
\sigma^2_{sample} = \frac{4}{4} = 1
\]
\[
\sigma_{sample} = \sqrt{1} = 1
\]

So, if you were looking for the standard deviation as if it were a sample, the answer would be **1**.

If considering the data as a whole population, your earlier computation (0.8944) is indeed correct. Please clarify if you're looking for sample or population standard deviation!