# Transferring percentage scores to raw scores

I have a question ranging from 1 to 5. I have 10 subjects, 6 persons select 4 and 4 persons select 5, So the average question is 4.4. If I calculate percentage for response modes ( 1 to 5), I get the following result

1  2  3  4   5
0  0  0 60  40


How I can get the values of 4.4 based on these percentages. Is that possible? Thank you for your help

• I'm not sure what you're asking for..Are you asking "how do I compute an average for values in a table? Is this an exercise for some class? – Glen_b Aug 21 '15 at 1:08
• @Glen- Based on the above table, how I can get 4.4 ( the average question). – User20100 Aug 21 '15 at 18:15
• How does that calculation relate to your title? – Glen_b Aug 22 '15 at 7:41

## 1 Answer

For tabulated values, where you have outcomes $x_i$ with proportions $p_i$:

 x    0   1   2   3   4   5
p    0   0   0   0  0.6 0.4
px    0   0   0   0  2.4 2.0


then the sample mean is $\sum_i p_i x_i=0+0+0+0+2.4+2.0=4.4$

This is entirely algebraically equivalent to writing out the ten scores 4,4,4,4,4,4,5,5,5,5 and averaging those