Calculations for Mean and Standard Deviations
|
x |
P (X = x) |
px [x × P (X = x)] |
x2 |
px2 [x2 × P (X = x)] |
|
− 10 |
|
= |
|
|
100 |
|
|
− 20 |
|
= |
|
|
400 |
|
|
30 |
|
= |
|
|
900 |
|
|
75 |
|
= |
|
|
5,625 |
|
|
80 |
|
= |
|
|
6,400 |
|
Total |
|
1 |
|
|
|
|
|
|
= 21.5 |
|
= 1,394.5 |
Since the given distribution is the probability distribution of a discrete random variable "X", Σ p = 1.
For the probability distribution:
Mean of the distribution
⇒ Expectation of the variable
Variance of the distribution
⇒ var (x) |
= |
E (x2) − (E(x))2 |
⇒ var (x) |
= |
Σ px2 − (Σ px)2 |
|
= |
1,394.5 − (21.5)2 |
|
= |
1,394.5 − 462.25 |
|
= |
932.25 |
Standard Deviation of the distribution
⇒ SD (x) |
= |
+ √ Var (x) |
⇒ SD (x) |
= |
+ √ 932.25 |
⇒ SD (x) |
= |
+ 30.53 |