Question

a veterinarian weighed a sample of 6 puppies. here are each of their weights (in kilograms): 2, 2, 7, 7, 10, 10. what is the standard - deviation? round your answer to three decimal places (or it will be marked incorrect). you may use the formula or statplot/desmos.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{2 + 2+7+7+10+10}{6}=\frac{38}{6}\approx6.333$.

Step2: Calculate the squared - differences

$(2 - 6.333)^2=(-4.333)^2 = 18.774889$, $(2 - 6.333)^2=18.774889$, $(7 - 6.333)^2=(0.667)^2 = 0.444889$, $(7 - 6.333)^2=0.444889$, $(10 - 6.333)^2=(3.667)^2 = 13.446889$, $(10 - 6.333)^2=13.446889$.

Step3: Calculate the variance

The variance $s^2=\frac{18.774889+18.774889 + 0.444889+0.444889+13.446889+13.446889}{6}=\frac{65.333334}{6}\approx10.889$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{10.889}\approx3.299$.

Answer:

$3.299$