The standard deviation of 7 scores 1,2,3,4,5,6,7 is

Options

A. 4
B. 2
C. `sqrt(7)`
D. 3

Answer

To find the standard deviation of the scores 1, 2, 3, 4, 5, 6, and 7, we will follow these steps:

### Step 1: Calculate the Mean (x̄)
The mean (x̄) is calculated by summing all the scores and dividing by the number of scores.

\[ x̄ = \frac{1 + 2 + 3 + 4 + 5 + 6 + 7}{7} \]

Calculating the sum:

\[ 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 \]

Now, divide by the number of scores (7):

\[ x̄ = \frac{28}{7} = 4 \]

### Step 2: Calculate the Deviations from the Mean
Next, we will calculate the deviations of each score from the mean, square those deviations, and then sum them up.

\[ \text{Deviations: } \begin{align*} (1 - 4)^2 & = (-3)^2 = 9 \\ (2 - 4)^2 & = (-2)^2 = 4 \\ (3 - 4)^2 & = (-1)^2 = 1 \\ (4 - 4)^2 & = (0)^2 = 0 \\ (5 - 4)^2 & = (1)^2 = 1 \\ (6 - 4)^2 & = (2)^2 = 4 \\ (7 - 4)^2 & = (3)^2 = 9 \\ \end{align*} \]

### Step 3: Sum the Squared Deviations
Now we will sum the squared deviations:

\[ 9 + 4 + 1 + 0 + 1 + 4 + 9 = 28 \]

### Step 4: Calculate the Variance
The variance (σ²) is the average of these squared deviations. Since we are dealing with a sample, we divide by the number of scores (n = 7).

\[ \sigma^2 = \frac{28}{7} = 4 \]

### Step 5: Calculate the Standard Deviation
Finally, the standard deviation (σ) is the square root of the variance.

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

### Conclusion
The standard deviation of the scores 1, 2, 3, 4, 5, 6, and 7 is **2**.

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