Question

calculate the standard deviation and variance of the data shown, to two decimal places.

x
17.6
11.4
19.3
2.9
18.9

standard deviation:
variance:
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Explanation:

Step1: Calculate the mean

First, sum all data points and divide by the count $n=5$.
$\bar{x} = \frac{17.6 + 11.4 + 19.3 + 2.9 + 18.9}{5} = \frac{70.1}{5} = 14.02$

Step2: Find squared deviations

Compute $(x_i - \bar{x})^2$ for each data point:
$(17.6-14.02)^2 = 3.58^2 = 12.8164$
$(11.4-14.02)^2 = (-2.62)^2 = 6.8644$
$(19.3-14.02)^2 = 5.28^2 = 27.8784$
$(2.9-14.02)^2 = (-11.12)^2 = 123.6544$
$(18.9-14.02)^2 = 4.88^2 = 23.8144$

Step3: Calculate variance

Average the squared deviations (sample variance is used here, dividing by $n-1$; if population, divide by $n$, but sample is standard for this type of problem):
$s^2 = \frac{12.8164 + 6.8644 + 27.8784 + 123.6544 + 23.8144}{5-1} = \frac{195.028}{4} = 48.757$

Step4: Calculate standard deviation

Take the square root of the variance:
$s = \sqrt{48.757} \approx 6.98$

Answer:

Standard deviation: 6.98
Variance: 48.76

Note: If using population variance (dividing by $n=5$), variance would be $\frac{195.028}{5}=39.01$, standard deviation $\sqrt{39.01}\approx6.25$. But sample variance is the standard default for this type of unlabeled dataset.