Question

Data sets A and B are dependent. Find sd.Assume that the paired data came from a population that is normally distributed.A. 1.73B. 1.21C. 1.32D. 1.89

Answer 1

The standard deviation for the paired data is 1.73

Using the data given

• A : 2.7, 3.7, 5.6, 2.6, 2.7

• B : 5.1, 4.0, 3.9, 3.8, 5.2

Difference between dataset A and B;

A - B

`X_(d)` = (A - B) = - 2.4, -0.3, 1.7, - 1.2, - 2.5

Sum of (A - B):

`Σ(X_(d))`= (-2.4 + (-0.3) + 1.7 + (-1.2) + (-2.5) = - 4. 7

Calcualting the Mean deviation

`M_(d)` = ΣXd / n = - 4.7 / 5 = - 0.94

Taking the difference ;

`X_(d) - M_(d)` = (-2.4 -(- 0.94)), (-0.3 -(-0.94)), (1.7 - (-0.94)), (-1.2 - (-0.94)), (-2.5 - (-0.94))

`(X_(d) - M_(d))` = - 1.46, 0.64, 2.64, - 0.26, - 1.56

Take the square of the difference;

`(X_(d) - M_(d))`² = (-1.46)²+ 0.64² + 2.64² + (-0.26)² + (-1.56)²

Take the sum of the squared difference;

Σ
`(X_(d) - M_(d))`² = (2.1316 + 0.4096 + 6.9696 + 0.0676 + 2.4336) = 12.012

We can then calculate the standard deviation

Standard deviation = √[Σ
`(X_(d) - M_(d))`² / (n-1)]

Standard deviation= √12.012 / 4

Standard deviation= 1.73

Therefore , the standard deviation is 1.73

Complete question :

Data sets A and B are dependent. Find sd.Assume that the paired data came from a population that is normally distributed.A. 1.73B. 1.21C. 1.32D. 1.89

A : 2.7, 3.7, 5.6, 2.6, 2.7

B : 5.1, 4.0, 3.9, 3.8, 5.2

Answer 2

Complete question :

A : 2.7, 3.7, 5.6, 2.6, 2.7

B : 5.1, 4.0, 3.9, 3.8, 5.2

Data sets A and B are dependent. Find sd.Assume that the paired data came from a population that is normally distributed.A. 1.73B. 1.21C. 1.32D. 1.89

Answer: A.1.73

Explanation:

Given the data:

A : 2.7, 3.7, 5.6, 2.6, 2.7

B : 5.1, 4.0, 3.9, 3.8, 5.2

Difference betweenA and B (A - B) :

Xd = (A - B) = - 2.4, -0.3, 1.7, - 1.2, - 2.5

Sum of (A - B) = Σ Xd = (-2.4 + (-0.3) + 1.7 + (-1.2) + (-2.5) = - 4. 7

Md = ΣXd / n = - 4.7 / 5 = - 0.94

Xd - Md = (-2.4 + 0.94), (-0.3 + 0.94), (1.7 + 0.94), (-1.2 + 0.94), (-2.5 + 0.94)

(Xd - Md) = - 1.46, 0.64, 2.64, - 0.26, - 1.56

(Xd - Md)^2 = (-1.46)^2 + 0.64^2 + 2.64^2 + (-0.26)^2 + (-1.56)^2

Σ(Xd - Md)^2 = (2.1316 + 0.4096 + 6.9696 + 0.0676 + 2.4336) = 12.012

Standard deviation = √[Σ(Xd - Md)^2 / (n-1)]

Standard deviation= √12.012 / 4

Standard deviation = 1.7329

Standard deviation= 1.73