Question

the tourist bureau of the caribbean islands surveyed a sample of 6 united states tourists as they left to return home. the tourists were asked how many days they spent on their visits. their responses were as follows. 7, 4, 12, 10, 9, 12 send data to calculator find the standard deviation of this sample of numbers. round your answer to two decimal places.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{7 + 4+12+10+9+12}{6}=\frac{54}{6}=9$.

Step2: Calculate the squared - differences

$(7 - 9)^2=(-2)^2 = 4$; $(4 - 9)^2=(-5)^2 = 25$; $(12 - 9)^2=3^2 = 9$; $(10 - 9)^2=1^2 = 1$; $(9 - 9)^2=0^2 = 0$; $(12 - 9)^2=3^2 = 9$.

Step3: Calculate the sum of squared - differences

$4+25 + 9+1+0+9=48$.

Step4: Calculate the sample variance

The sample variance $s^2=\frac{48}{6 - 1}=\frac{48}{5}=9.6$.

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{9.6}\approx3.10$.

Answer:

$3.10$