Answer:
Step-by-step explanation:
Given the sample data 2 6 15 9 11 22 1 4 8 19, before we can get the standard deviation, we need to first calculate the mean.
mean = 2 +6 +15 +9 +11 +22 +1 +4 +8 +19/10
mean = 97/10
mean = 9.7
Standard deviation for ungrouped data is expressed using the formula;
[tex]S = \sqrt{ \dfrac{\sum(x-\overline x)^2}{n-1} }[/tex]
[tex]\overline x \ is\ the \ mean\\n \ is \ sample \ size[/tex]
[tex]S = \sqrt{\frac{(2-9.7)^2+(6-9.7)^2+(15-9.7)^2+(9-9.7)^2+(11-9.7)^2+(22-9.7)^2+(1-9.7)^2+(4-9.7)^2+(8-9.7)^2+(19-9.7)^2}{10-1} }\\ S = \sqrt{\frac{(-7.7)^2+(-3.7)^2+(5.3)^2+(-0.7)^2+(1.3)^2+(12.3)^2+(-8.7)^2+(-5.7)^2+(-1.7)^2+(9.3)^2}{10-1} }\\\\S = \sqrt{\dfrac{59.29+13.69+28.09+0.49+1.69+151.29+75.69+32.49+2.89+86.49}{10-1} }\\\\\\S = \sqrt{\dfrac{452.1}{9} }\\\\S = \sqrt{50.23}\\ \\S = 7.08\\\\S \approx 7.1[/tex]
Hence the standard deviation of the sample data is 7.1
