question 7
the numbers of false fire alarms were counted each month at a sample of sites. the results are given in
the following table.
14 13 8 14 11
7 7 12 5 6
12 11 13 13 6
8 12
label the following numerical measures according to the context:
size: ?
mean: ?
variance: ?
standard deviation: ?
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Question

Accepted Answer

# Explanation:
## Step1: Calculate the size of the data set
Count the number of data points. There are $14$ data points.
## Step2: Calculate the mean $\bar{x}$
$$
\begin{align*}
\bar{x}&=\frac{14 + 13+8+14+11+7+7+12+5+6+12+11+13+13+6+8+12}{17}\
&=\frac{198}{17}\approx 11.65
\end{align*}
$$
## Step3: Calculate the variance $s^{2}$
$$
\begin{align*}
s^{2}&=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n-1}\
&=\frac{(14 - 11.65)^{2}+(13 - 11.65)^{2}+(8 - 11.65)^{2}+(14 - 11.65)^{2}+(11 - 11.65)^{2}+(7 - 11.65)^{2}+(7 - 11.65)^{2}+(12 - 11.65)^{2}+(5 - 11.65)^{2}+(6 - 11.65)^{2}+(12 - 11.65)^{2}+(11 - 11.65)^{2}+(13 - 11.65)^{2}+(13 - 11.65)^{2}+(6 - 11.65)^{2}+(8 - 11.65)^{2}+(12 - 11.65)^{2}}{16}\
&=\frac{5.5225 + 1.8225+13.3225 + 5.5225+0.4225+21.6225+21.6225+0.1225+44.2225+31.9225+0.1225+0.4225+1.8225+1.8225+31.9225+13.3225+0.1225}{16}\
&=\frac{202.1175}{16}\approx12.63
\end{align*}
$$
## Step4: Calculate the standard deviation $s$
$$s=\sqrt{s^{2}}=\sqrt{12.63}\approx3.55$$

# Answer:
Size: $17$
Mean: $\approx11.65$
Variance: $\approx12.63$
Standard deviation: $\approx3.55$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the size of the data set

Step2: Calculate the mean \(\bar{x}\)

Step3: Calculate the variance \(s^{2}\)

Step4: Calculate the standard deviation \(s\)

Answer: