Respuesta :
Answer:
The standard deviation of the weight, σ, is approximately 4.73 kg
Step-by-step explanation:
The weights of the six puppies are;
[tex]x_i[/tex] = 1, 2, 7, 7, 10, and 15
The number of puppies, n = 6
Therefore, we have;
The mean = μ = ∑x/n = (1 + 2 + 7 + 7 + 10 + 15)/6 = 7
The standard deviation, σ, is given as follows;
[tex]\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{n}}[/tex]
By substituting, we have;
[tex]\sigma =\sqrt{\dfrac{ \left (1-7 \right )^{2} + \left (2-7 \right )^{2} + \left (7-7 \right )^{2} + \left (7-7 \right )^{2} + \left (10-7 \right )^{2} + \left (15-7 \right )^{2} }{6}}[/tex]
Simplifying gives;
[tex]\sigma =\sqrt{\dfrac{ \left (-6 \right )^{2} + \left (-5 \right )^{2} + \left (0 \right )^{2} + \left (0 \right )^{2} + \left (3 \right )^{2} + \left (8 \right )^{2} }{6}} =\sqrt{\dfrac{ 36 + 25 + 0 +0+ 9 + 64 }{6}}[/tex]
[tex]\sigma =\sqrt{\dfrac{ 134 }{6}} = \sqrt{\dfrac{67}{3} } \approx 4.72582[/tex]
The standard deviation of the weight, σ ≈ 4.73 kg to two decimal places.
