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 $x_i$ $(x_i - ?)^2$ 1 10 $(10 - )^2=0.36$ 2 10 0.36 3 15 4 7 12.96 5 = ? 0.16 average: ? = total = variance: ? = total/? = st. dev.: ? = 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 $x_i$ $(x_i - ?)^2$ 1 10 $(10 - )^2=0.36$ 2 10 0.36 3 15 4 7 12.96 5 = ? 0.16 average: ? = total = variance: ? = total/? = st. dev.: ? = question help: video written example message instructor post to forum submit question

Answer

Explanation:

Step1: Calculate the sample mean

The sample data is (x_1 = 10,x_2 = 10,x_3 = 15,x_4 = 7,x_5 = 11). The formula for the sample mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}), where (n = 5). (\bar{x}=\frac{10 + 10+15+7+11}{5}=\frac{53}{5}=10.6)

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

  • 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)

(Total=0.36 + 0.36+19.36+12.96+0.16=33.2)

Step4: Calculate the sample variance (s^2)

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

Step5: Calculate the sample standard - deviation (s)

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

Answer:

(2.88)