Calculation: WNXwUK - 1
s^2 =
| ( (x1-x_v)^2* m1+ (x2-x_v)^2* m2+ (x3-x_v)^2* m3) |
| / (n-1) |
|
s^2 =
$$s^{2}$$ = $$\frac{(x1-x_{v})^{2}\cdot m1+(x2-x_{v})^{2}\cdot m2+(x3-x_{v})^{2}\cdot m3}{n-1}$$
| ( (x1-x_v)^2* m1+ (x2-x_v)^2* m2+ (x3-x_v)^2* m3) |
| / (n-1) |
s^2 =
-
+
+
-
+
+
-
+
$$s^{2}$$ = $$\frac{x1^{2}\cdot m1}{n-1}-\frac{2\cdot x1\cdot x_{v}\cdot m1}{n-1}+\frac{x_{v}^{2}\cdot m1}{n-1}+\frac{x2^{2}\cdot m2}{n-1}-\frac{2\cdot x2\cdot x_{v}\cdot m2}{n-1}+\frac{x_{v}^{2}\cdot m2}{n-1}+\frac{x3^{2}\cdot m3}{n-1}-\frac{2\cdot x3\cdot x_{v}\cdot m3}{n-1}+\frac{x_{v}^{2}\cdot m3}{n-1}$$
| x1^2* m1 |
| / (n-1) |
| 2* x1* x_v* m1 |
| / (n-1) |
| x_v^2* m1 |
| / (n-1) |
| x2^2* m2 |
| / (n-1) |
| 2* x2* x_v* m2 |
| / (n-1) |
| x_v^2* m2 |
| / (n-1) |
| x3^2* m3 |
| / (n-1) |
| 2* x3* x_v* m3 |
| / (n-1) |
| x_v^2* m3 |
| / (n-1) |
s = saknis(
-
+
+
-
+
+
-
+
)$$s$$ = $$\sqrt {\frac{x1^{2}\cdot m1}{n-1}-\frac{2\cdot x1\cdot x_{v}\cdot m1}{n-1}+\frac{x_{v}^{2}\cdot m1}{n-1}+\frac{x2^{2}\cdot m2}{n-1}-\frac{2\cdot x2\cdot x_{v}\cdot m2}{n-1}+\frac{x_{v}^{2}\cdot m2}{n-1}+\frac{x3^{2}\cdot m3}{n-1}-\frac{2\cdot x3\cdot x_{v}\cdot m3}{n-1}+\frac{x_{v}^{2}\cdot m3}{n-1}}$$
| x1^2* m1 |
| / (n-1) |
| 2* x1* x_v* m1 |
| / (n-1) |
| x_v^2* m1 |
| / (n-1) |
| x2^2* m2 |
| / (n-1) |
| 2* x2* x_v* m2 |
| / (n-1) |
| x_v^2* m2 |
| / (n-1) |
| x3^2* m3 |
| / (n-1) |
| 2* x3* x_v* m3 |
| / (n-1) |
| x_v^2* m3 |
| / (n-1) |
s = saknis(
-
+
+
-
+
+
-
+
)$$s$$ = $$\sqrt {\frac{m1\cdot x1^{2}}{n-1}-\frac{2\cdot m1\cdot x1\cdot x_{v}}{n-1}+\frac{m1\cdot x_{v}^{2}}{n-1}+\frac{m2\cdot x2^{2}}{n-1}-\frac{2\cdot m2\cdot x2\cdot x_{v}}{n-1}+\frac{m2\cdot x_{v}^{2}}{n-1}+\frac{m3\cdot x3^{2}}{n-1}-\frac{2\cdot m3\cdot x3\cdot x_{v}}{n-1}+\frac{m3\cdot x_{v}^{2}}{n-1}}$$
| m1* x1^2 |
| / (n-1) |
| 2* m1* x1* x_v |
| / (n-1) |
| m1* x_v^2 |
| / (n-1) |
| m2* x2^2 |
| / (n-1) |
| 2* m2* x2* x_v |
| / (n-1) |
| m2* x_v^2 |
| / (n-1) |
| m3* x3^2 |
| / (n-1) |
| 2* m3* x3* x_v |
| / (n-1) |
| m3* x_v^2 |
| / (n-1) |