Chapter 3: Q 3.77 (page 114)

Determine the age and sample standard deviation for each of the due sets. For the sample standard deviation round each answer to one more decimal place than that used for the observation.
The Beatles. The English rock band, The Beatles, was formed in Liverpool in 1960. There are 12 studio albums that are considered part of their core catalogue In the article. "Length of The Beatles' Songs" (Chance, Vol. 25. No. 1. pp. 30-33), T. Koyama lists the album title, date of release, and number of songs on each album. Here are the album names and numbers of songs.

Short Answer

Expert verified

Range of the data $= 24$

Standard deviation of the data $= 5$

Step by step solution

Step 1. Given information.

We have given data: $14, 14, 13, 14, 14, 14, 14, 13, 30, 6, 17, 12$

Step 2. To find range of the data.

$R a n g e = M a x . V a l u e - M i n . v a l u e = 30 - 6 = 24$

Step 3. To find mean of the data.

$M e a n = \frac{S u m o f o b s e r v a t i o n}{N u m b e r o f o b s e r v a t i o n} = \frac{14 + 14 + 13 + 14 + 14 + 14 + 14 + 13 + 30 + 6 + 17 + 12}{12} = \frac{175}{12} = 14.58$

Step 4. To find standard deviation of the data.

$x$	$x - x$	${(x - x)}^{2}$
$14 14 13 14 14 14 14 13 30 6 17 12$	$- 0.58 - 0.58 - 1.58 - 0.58 - 0.58 - 0.58 - 0.58 - 1.58 15.42 - 8.58 2.42 - 2.58$	$0.34 0.34 2.50 0.34 0.34 0.34 0.34 2.50 237.78 73.62 5.86 6.66$

localid="1652001456214" $S \tan d a r d d e r i v a t i o n = \sqrt{\frac{\sum_{} {(x - x)}^{2}}{n - 1}} = \sqrt{\frac{330.92}{13 - 1}} = \sqrt{\frac{1521.71}{12}} = \sqrt{27.58} = 5$