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 15.7 songs.
(type an integer or a decimal. round to one decimal place as needed.)

b. find the median.
the median is 14 songs.
(type an integer or a decimal. round to one decimal place as needed.)

c. find the mode. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
● a. the mode(s) is/are □ songs.
(use a comma to separate answers as needed.)
● b. there is no mode.

table: number of songs
album | number of songs
revolver | 14
a hard day’s night | 13
rubber soul | 14
with the beatles | 14
please please me | 14
help! | 14
abbey road | 17
the beatles | 30
beatles for sale | 14
sgt. pepper | 13

Explanation:

Part (a): Find the mean

Step 1: List the number of songs

The number of songs for each album are: 14, 13, 14, 14, 14, 14, 17, 30, 14, 13.

Step 2: Calculate the sum

Sum = \(14 + 13 + 14 + 14 + 14 + 14 + 17 + 30 + 14 + 13\)
First, add the 14s: There are 6 fours (wait, 14 appears how many times? Let's count: Revolver (14), Rubber Soul (14), With the Beatles (14), Please Please Me (14), Help! (14), Beatles for Sale (14) → that's 6 times 14. Then 13 (A Hard Day's Night), 13 (Sgt. Pepper), 17 (Abbey Road), 30 (The Beatles). So sum = \(6\times14 + 2\times13 + 17 + 30\)
\(6\times14 = 84\), \(2\times13 = 26\), so total sum = \(84 + 26 + 17 + 30 = 157\)

Step 3: Calculate the mean

Mean = \(\frac{\text{Sum}}{\text{Number of albums}}\) = \(\frac{157}{10} = 15.7\)

Step 1: Arrange the data in ascending order

The data points (number of songs) are: 13, 13, 14, 14, 14, 14, 14, 14, 17, 30.

Step 2: Find the middle value(s)

Since there are 10 data points (even number), the median is the average of the 5th and 6th values.
The 5th value is 14, the 6th value is 14.

Step 3: Calculate the median

Median = \(\frac{14 + 14}{2} = 14\)

Step 1: Count the frequency of each value

• 13: appears 2 times
• 14: appears 6 times
• 17: appears 1 time
• 30: appears 1 time

Step 2: Identify the mode(s)

The value with the highest frequency is 14 (appears 6 times), which is more than the frequency of any other value.

Answer:

15.7

Part (b): Find the median