Question

herman recorded the weights of 7 of his classmates pets. he recorded:
1 pound 1 pound 5 pounds 7 pounds 3 pounds 8 pounds 3 pounds
what was the standard deviation of the weights of the pets, in pounds?
if the answer is a decimal, round it to the nearest tenth.
standard deviation (σ): pounds
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Explanation:

Step1: Calculate the mean

The mean \(\bar{x}=\frac{1 + 1+5 + 7+3 + 8+3}{7}=\frac{28}{7} = 4\)

Step2: Calculate the squared differences

\((1 - 4)^2=(- 3)^2 = 9\), \((1 - 4)^2=(-3)^2 = 9\), \((5 - 4)^2=(1)^2 = 1\), \((7 - 4)^2=(3)^2 = 9\), \((3 - 4)^2=(-1)^2 = 1\), \((8 - 4)^2=(4)^2 = 16\), \((3 - 4)^2=(-1)^2 = 1\)

Step3: Calculate the variance

The variance \(\sigma^{2}=\frac{9+9 + 1+9+1+16+1}{7}=\frac{46}{7}\approx6.57\)

Step4: Calculate the standard deviation

The standard deviation \(\sigma=\sqrt{\frac{46}{7}}\approx2.6\)

Answer:

\(2.6\)