Question

Two 5-sided dice are rolled and the sides are added. Find the mean and the standard-deviation

Answer 1

The dataset consists of all the possible combinations:

1+1=2; 1+2=3; 1+3=4; 1+4=5; 1+5=6;

2+1=3; 2+2=4; 2+3=5; 2+4=6; 2+5=7;

3+1=4; 3+2=5; 3+3=6; 3+4=7; 3+5=8;

4+1=5; 4+2=6; 4+3=7; 4+4=8; 4+5=9;

5+1=6; 5+2=7; 5+3=8; 5+4=9; 5+5=10.
 

The scores range between 2 and 10 with the following frequency distribution:

2: 1

3: 2

4: 3

5: 4

6: 5

7: 4

8: 3

9: 2

10: 1

The mean is (1*2+2*3+3*4+4*5+5*6+4*7+3*8+2*9+1*10)/25=(2+6+12+20+30+28+24+18+10)/25=150/25=6.

The standard deviation is sqrt(1*(-4)^2+2*(-3)^2+3*(-2)^2+4*(-1)^2+5*0+4*1^2+3*2^2+2*3^2+1*4^2)/25)=

sqrt(32+36+24+8+0)/5=sqrt(100)/5=2.

Mean is 6 and SD is 2.