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vekshin1
3 years ago
10

Find the sample standard deviation:

Mathematics
1 answer:
zlopas [31]3 years ago
7 0

Answer:

<h2>B. 7.1</h2>

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;

S = \sqrt{ \dfrac{\sum(x-\overline x)^2}{n-1} }

\overline x \ is\ the \ mean\\n \ is \ sample \ size

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

<em>Hence the standard deviation of the sample data is 7.1</em>

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OK.  All the work is in the attached drawing.

Please spend enough time with it to understand what was done and how, so that you can do the next problem like this one completely on your own.

Good luck !

==============================

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