Determine The Standard Deviation of Scores correct to 2 decimal places.

Your calculation $\frac{20}{6} = 3.33$ is correct for $\frac{\sum d_i}{n}$, which is a correction factor for the mean, not the mean itself. The actual mean $\bar{x} = A + \frac{\sum d_i}{n} = 15 + 3.33 = 18.33$. However, this does not affect the standard deviation calculation using the assumed mean method.

Your calculation $\frac{430}{6} = 71.67$ is correct for $\frac{\sum d_i^2}{n}$.

Rounding to two decimal places, $V \approx 60.58$. Your calculation is correct.

Rounding to two decimal places, $\sigma \approx 7.78$. Your calculation is correct.

The standard deviation is $\boxed{7.78}$.

9. The equation of a circle

The equation of the circle is given as $x^2+y^2-4x+6y+4=0$.

To complete the square for $x^2-4x$, add $\left(\frac{-4}{2}\right)^2 = (-2)^2 = 4$.
To complete the square for $y^2+6y$, add $\left(\frac{6}{2}\right)^2 = (3)^2 = 9$.
Add these values to both sides of the equation.

Your work matches this step perfectly.

The standard form of a circle's equation is $(x-h)^2 + (y-k)^2 = r^2$, where $(h,k)$ is the center and $r$ is the radius.
Comparing this to $(x-2)^2 + (y+3)^2 = 9$:
The center of the circle is $(h,k) = (2, -3)$.
The radius of the circle is $r = \sqrt{9} = 3$.

To draw the circle:

• Plot the center point at $(2, -3)$ on the grid.
• From the center, measure 3 units in all four cardinal directions (up, down, left, right) to mark points $(2, 0)$, $(2, -6)$, $(-1, -3)$, and $(5, -3)$.
• Sketch a smooth curve connecting these points to form the circle.

The center of the circle is $\boxed{(2, -3)}$ and the radius is $\boxed{3}$.