Question

calculate the standard deviation for a sample with 11 scores: 12, 7, 5, 16, 8, 10, 14, 6, 11, 9, 12. (round to two decimal places if necessary)

3.41
3.25
10.55
11.60

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{12 + 7+5+16+8+10+14+6+11+9+12}{11}=\frac{110}{11} = 10$.

Step2: Calculate the squared - differences

$(12 - 10)^2=4$, $(7 - 10)^2 = 9$, $(5 - 10)^2=25$, $(16 - 10)^2 = 36$, $(8 - 10)^2=4$, $(10 - 10)^2 = 0$, $(14 - 10)^2=16$, $(6 - 10)^2 = 16$, $(11 - 10)^2=1$, $(9 - 10)^2 = 1$, $(12 - 10)^2=4$.

Step3: Calculate the sum of squared - differences

$4+9+25+36+4+0+16+16+1+1+4=116$.

Step4: Calculate the sample variance

The sample variance $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}=\frac{116}{11 - 1}=\frac{116}{10}=11.6$.

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{11.6}\approx3.41$.

Answer:

A. 3.41