Question

section 4.5 homework
score: 5.31/9 answered: 6/9
question 7
find the sample variance of the data: (round the answer to 2 decimal places)
8, 6, 11, 8, 15, 5, 10, 7, 13, 8, 9, 15, 6
the sample variance: select an answer =
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Explanation:

Step1: Calculate the mean

First, sum the data values: $8 + 6+11 + 8+15+5+10+7+13+8+9+15+6=111$. There are $n = 13$ data - points. The mean $\bar{x}=\frac{111}{13}\approx8.54$.

Step2: Calculate the squared - differences

For each data - point $x_i$, calculate $(x_i-\bar{x})^2$.
For $x_1 = 8$: $(8 - 8.54)^2=(-0.54)^2 = 0.2916$.
For $x_2 = 6$: $(6 - 8.54)^2=(-2.54)^2 = 6.4516$.
For $x_3 = 11$: $(11 - 8.54)^2=(2.46)^2 = 6.0516$.
For $x_4 = 8$: $(8 - 8.54)^2=(-0.54)^2 = 0.2916$.
For $x_5 = 15$: $(15 - 8.54)^2=(6.46)^2 = 41.7316$.
For $x_6 = 5$: $(5 - 8.54)^2=(-3.54)^2 = 12.5316$.
For $x_7 = 10$: $(10 - 8.54)^2=(1.46)^2 = 2.1316$.
For $x_8 = 7$: $(7 - 8.54)^2=(-1.54)^2 = 2.3716$.
For $x_9 = 13$: $(13 - 8.54)^2=(4.46)^2 = 19.8916$.
For $x_{10}=8$: $(8 - 8.54)^2=(-0.54)^2 = 0.2916$.
For $x_{11}=9$: $(9 - 8.54)^2=(0.46)^2 = 0.2116$.
For $x_{12}=15$: $(15 - 8.54)^2=(6.46)^2 = 41.7316$.
For $x_{13}=6$: $(6 - 8.54)^2=(-2.54)^2 = 6.4516$.
Sum these squared - differences: $0.2916+6.4516+6.0516+0.2916+41.7316+12.5316+2.1316+2.3716+19.8916+0.2916+0.2116+41.7316+6.4516 = 130.84$.

Step3: Calculate the sample variance

The formula for the sample variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}$. Here, $n = 13$, so $s^2=\frac{130.84}{13 - 1}=\frac{130.84}{12}\approx10.90$.

Answer:

$10.90$