the numbers of false fire alarms were counted each month at a sample of sites. the results are given in the…

the numbers of false fire alarms were counted each month at a sample of sites. the results are given in the following table. 10 10 15 7 11 compute the value of the sample standard deviation using the table below: (round the answers to 2 decimal places) i $x_i$ $(x_i - \text{?})^2$ 1 10 $(10 - square)^2 = 0.36$ 2 10 0.36 3 15 $square$ 4 7 12.96 5 = $\text{?}$ $square$ 0.16 average: $\text{?}$ = $square$ total = $square$ variance: $\text{?}$ = total/$\text{?}$ = $square$ st. dev.: $\text{?}$ = $square$ question help: video written example message instructor post to forum submit question

the numbers of false fire alarms were counted each month at a sample of sites. the results are given in the following table. 10 10 15 7 11 compute the value of the sample standard deviation using the table below: (round the answers to 2 decimal places) i $x_i$ $(x_i - \text{?})^2$ 1 10 $(10 - square)^2 = 0.36$ 2 10 0.36 3 15 $square$ 4 7 12.96 5 = $\text{?}$ $square$ 0.16 average: $\text{?}$ = $square$ total = $square$ variance: $\text{?}$ = total/$\text{?}$ = $square$ st. dev.: $\text{?}$ = $square$ question help: video written example message instructor post to forum submit question

Answer

Explanation:

Step1: Calculate the average

The data set is (10, 10, 15, 7, 11). The sum of the data is (10 + 10+15 + 7+11=53). There are (n = 5) data - points. The average (\bar{x}=\frac{53}{5}=10.6).

Step2: Calculate ((x_i-\bar{x})^2) for each data - point

  • For (x_1 = 10), ((10 - 10.6)^2=(- 0.6)^2 = 0.36)
  • For (x_2 = 10), ((10 - 10.6)^2=(-0.6)^2 = 0.36)
  • For (x_3 = 15), ((15 - 10.6)^2=(4.4)^2 = 19.36)
  • For (x_4 = 7), ((7 - 10.6)^2=(-3.6)^2 = 12.96)
  • For (x_5 = 11), ((11 - 10.6)^2=(0.4)^2 = 0.16)

Step3: Calculate the total of ((x_i-\bar{x})^2)

The total is (0.36+0.36 + 19.36+12.96+0.16=33.2)

Step4: Calculate the sample variance

The sample variance (s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}). Here, (n = 5), so (s^2=\frac{33.2}{4}=8.3)

Step5: Calculate the sample standard deviation

The sample standard deviation (s=\sqrt{s^2}=\sqrt{8.3}\approx2.88)

Answer:

(2.88)