Question

calculate the standard deviation for a sample with 11 scores: 3, 4, 6, 7, 9, 11, 12, 13, 17, 19, 20. (round to two decimal places if necessary) 5.59 5.87 31.27 34.40

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{3 + 4+6+7+9+11+12+13+17+19+20}{11}=\frac{121}{11} = 11$.

Step2: Calculate the squared - differences

$(3 - 11)^2=(-8)^2 = 64$, $(4 - 11)^2=(-7)^2 = 49$, $(6 - 11)^2=(-5)^2 = 25$, $(7 - 11)^2=(-4)^2 = 16$, $(9 - 11)^2=(-2)^2 = 4$, $(11 - 11)^2=0^2 = 0$, $(12 - 11)^2=1^2 = 1$, $(13 - 11)^2=2^2 = 4$, $(17 - 11)^2=6^2 = 36$, $(19 - 11)^2=8^2 = 64$, $(20 - 11)^2=9^2 = 81$.

Step3: Calculate the sum of squared - differences

$S=\sum_{i = 1}^{n}(x_i-\bar{x})^2=64 + 49+25+16+4+0+1+4+36+64+81=344$.

Step4: Calculate the sample variance

The sample variance $s^2=\frac{S}{n - 1}=\frac{344}{11-1}=\frac{344}{10}=34.4$.

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{s^2}=\sqrt{34.4}\approx5.87$.

Answer:

5.87