Prove that XZ bisects angle WZY given that W, X, Y, and Z are points on a circle and WX = YX. Calculate the standard deviation for the dataset 2, 7, 5, 6, 9.

We are given that points W, X, Y, and Z lie on a circle. We are also given that the chord WX is equal in length to the chord YX ($WX = YX$).

In a circle, equal chords subtend equal arcs. Since $WX = YX$, the arc WX is equal to the arc YX.

Angles subtended by equal arcs at any point on the remaining part of the circumference are equal.
The angle $\angle WZX$ is subtended by arc WX at point Z on the circumference.
The angle $\angle YZX$ is subtended by arc YX at point Z on the circumference.

Since arc WX = arc YX, it follows that the angles they subtend at Z are equal:

An angle is bisected if it is divided into two equal angles. Since $\angle WZX$ and $\angle YZX$ are the two parts of $\angle WZY$, and they are equal, the line segment XZ bisects $\angle WZY$.

Therefore, XZ bisects angle WZY.

: Standard Deviation

The data set is $x = \{2, 7, 5, 6, 9\}$.
The number of data points is $N = 5$.

The mean is the sum of all data points divided by the number of data points.

For $x_1 = 2$: $(2 - 5.8)^2 = (-3.8)^2 = 14.44$
For $x_2 = 7$: $(7 - 5.8)^2 = (1.2)^2 = 1.44$
For $x_3 = 5$: $(5 - 5.8)^2 = (-0.8)^2 = 0.64$
For $x_4 = 6$: $(6 - 5.8)^2 = (0.2)^2 = 0.04$
For $x_5 = 9$: $(9 - 5.8)^2 = (3.2)^2 = 10.24$

The population variance is the sum of the squared differences divided by $N$.

The standard deviation is the square root of the variance.

Rounding to two decimal places:

The standard deviation of the data is $\boxed{2.32}$.