Question

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,\ t. koyama lists the album title, date of release, and number of songs on each album. find the mean, median and mode(s) of the data. the album names and numbers of songs for 10 albums are available below. complete parts (a) through (c) below.
click the icon to view the number of songs for each album.

a. find the mean.
the mean is \boxed{} songs.
(type an integer or a decimal. round to one decimal place as needed.)

Explanation:

To solve this, we need the number of songs for each of the 10 albums. Since the data isn't provided here, I'll assume we have the counts. Let's denote the number of songs as \( x_1, x_2, \dots, x_{10} \).

Step 1: Recall the formula for the mean

The mean (\(\bar{x}\)) of a set of data is calculated by the formula:
\[
\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}
\]
where \( n = 10 \) (number of albums) and \( \sum_{i=1}^{n} x_i \) is the sum of the number of songs in each album.

Step 2: Sum the number of songs

Suppose the number of songs for the 10 albums are (for example, typical Beatles album song counts: 14, 14, 13, 14, 12, 14, 13, 14, 11, 14). Let's sum these:
\( 14 + 14 + 13 + 14 + 12 + 14 + 13 + 14 + 11 + 14 \)
\( = (14 \times 7) + 13 + 13 + 12 + 11 \)
\( = 98 + 13 + 13 + 12 + 11 \)
\( = 98 + 49 \)
\( = 147 \)

Step 3: Calculate the mean

Using \( n = 10 \) and sum \( = 147 \):
\[
\bar{x} = \frac{147}{10} = 14.7
\]

(Note: If the actual song counts differ, substitute the correct values into the sum. For example, if the data is different, recalculate the sum and divide by 10.)

Answer:

Assuming the sum of songs is 147 (for the example data), the mean is \(\boldsymbol{14.7}\) songs.

(If you provide the actual number of songs for each album, we can compute the exact mean.)