Question

Every year, the students at a school are given a musical aptitude test that rates them from 0 (no musical aptitude) to 5 (high musical aptitude). This year's results were: Aptitude Score Frequency 0 1 1 2 2 2 3 2 4 3 5 4 The mean ( ¯ x ) aptitude score

Answer 1

The mean aptitude score is 3.14.

Explanation:

The given frequency table is

Aptitude Score : 0 1 2 3 4 5

Frequency : 1 2 2 2 3 4

Formula for Mean

`Mean=(\sum f_ix_i)/(\sum f_i)`

First find
`\sum f_ix_i\text{ and }\sum f_i`.

`x\quad\quad f_i \quad\quad f_ix_i`

0 1 0

1 2 2

2 2 4

3 2 6

4 3 12

5 4 20

Sum = 14 44

Substitute
`\sum f_ix_i=44\text{ and }\sum f_i=14` in the above formula.

`Mean=(44)/(14)`

`Mean\approx 3.14`

Therefore, the mean aptitude score is 3.14.