Give me some time to think

Alright , the total no. Of out comes will be:

$1+2+3 +4=10$

$1+ 2+ 3×4=15$

$1+ 2× 3+4=11$

$1+ 2×3 ×4=25$

$1×2 + 3+4=9$

$1× 2+ 3×4=14$

$1×2 × 3+4=10$

$1× 2× 3×4=24$

Total $=118$

Mean $=\frac{118}{8}=\boxed{14.75}$ .

If anybody has a doubt on the upper bound of the number of outcomes, then treat $+$ as binary 0 and $-$ as binary 1. Then we know that for a three bit binary system, the number of outcomes produced are eight. i.e.

$0 \quad 0 \quad 0 \quad$

$0 \quad 0 \quad 1 \quad$

$0 \quad 1 \quad 0 \quad$

$0 \quad 1 \quad 1 \quad$

$1 \quad 0 \quad 0 \quad$

$1 \quad 0 \quad 1 \quad$

$1 \quad 1 \quad 0 \quad$

$1 \quad 1 \quad 1 \quad$

Now replace all $0's$ with $+$ and all $1's$ with $\times$ , and place $1, 2, 3, 4$ in the each expression, you will get the same outcomes in the same manner as shown above.