# Download Mean E(X) = ∑ . Standard Deviation: 1 ∑ (x − x) 2 = E(X 2) − E(X

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```P
x
x∈X
Mean E(X) =
n
Standard Deviation:
1
n
.
P
x∈X (x
− x)2 = E(X 2 ) − E(X)2 .
S1 = {70, 65, 68, 69, 70},
S2 = {66, 69, 65, 66, 64}.
Sample Mean
1
n
Pn
i=1
xi
70 + 65 + 68 + 69 + 70
= 68.4.
5
66 + 69 + 65 + 66 + 64
x2 =
= 66.0.
5
x1 =
Sample Standard Deviation
n
s21 =
1 X
= (xi − x)2 .
n − 1 i=1
(1.6)2 + (−3.4)2 + (−0.4)2 + (0.6)2 + (1.6)2
2.56 + 11.56 + 0.16 + 0.36 + 2.56
s21 = 17.20
Sample Variance s21 = 17.2, sample standard deviation s1 =
√
17.2 ≈ 4.15.
s22 = 02 + 32 + (−1)2 + 02 + (−2)2 = 14.
√
Sample Variance s22 = 14,
√ s2√= 14 ≈ 3.74.
Mean
s1 / n, 3.44 ≈ 1.85
√
√ variance
s2 / n = 2.8 ≈ 1.67.
Are Sample means different?
x − x2
2.4
2.4
2.4
q 12
≈ 0.96.
≈
=√
=√
2
s1
s2
2.498
3.44 + 2.8
6.24
+
n1
n2
No, the sample means are less than two standard deviations apart. Therefore the
means do not differ in a statistically significant way.
1
```
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