Q 3-25. - Elementary Statistics

Question

Find the 

a. Mean    b. median      c. mode

For the mean and the median, round each answer to one more decimal place than that used for the observations.

 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" . 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.

Step-by-Step Solution

Answer

$$\begin{gathered} a) 14.6 \\ b) 14 \\ c) 14 \end{gathered}$$

Step 1. Given information.

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

Step 2. Mean of the data.

Mean 

$$\begin{gathered} =\frac{14+14+13+14+14+14+14+13+30+6+17+12}{12} \\ =\frac{175}{12} \\ =14.6 \end{gathered}$$

Step 3. Median of the data.

Arrange the data in increasing order : $6, 12, 13, 13, 14, 14, 14, 14, 14, 14, 17, 30$

Median

$$\begin{gathered} =\frac{6th+7th}{2} \\ =\frac{14+14}{2} \\ =\frac{28}{2} \\ =14 \end{gathered}$$

Step 4. Mode of the data.

The greatest frequency is the mode of the data set .

The greatest frequency is $6$. Hence the mode is $14$.