Question

Question 6 (1.1 points) Following are the playback time, in hours, for a sample of MP3 players. Calculate the sample standard deviation. 23, 19, 18, 18, 25, 21, 28, 28 Write only a number as your answer. Round to two decimal places (for example: 8.32) Your Answer:

Answer 1

$\\ To \ find \ standard \ deviation \ we \ use \ the \ following \ formula\\ \\ \sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } \\\\\ \ Step \ 1: \ Find \ the \ mean. \\ \\ Mean (\overline X)=\frac{23+19+18+18+25+21+28+28}{8}=\frac{180}{8}=22.5\\ \\ Step \ 2: \ Create \ the \ following \ table.\ \\$

data	data-mean	(data - mean)2
23	0.5	0.25
19	-3.5	12.25
18	-4.5	20.25
18	-4.5	20.25
25	2.5	6.25
21	-1.5	2.25
28	5.5	30.25
28	5.5	30.25

$\\ Step \ 3: \ Find \ the \ sum \ of \ numbers \ in \ the \ last \ column \ to \ get.\\ \sum{\left(x_i - \overline{X}\right)^2} = 122\\ \\ Step \ 4: \ Calculate \ \sigma \ using \ the \ above \ formula.\\ \sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 122 }{ 8 - 1} } \approx 4.1748$

$\\ \boldsymbol{4.17}$