If mean of is 10then which is the mean of last four scores?

Correct option is D

Step 1: Calculate xxx using the given information The given scores are: x,x+4,x+7,2x+5,x+10x, x+4, x+7, 2x+5, x+10x,x+4,x+7,2x+5,x+10. The mean of these scores is given as 10.
Formula for mean: Mean=Sum of all scoresNumber of scores\text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}}Mean=Number of scoresSum of all scores​ 10=x+(x+4)+(x+7)+(2x+5)+(x+10)510 = \frac{x + (x+4) + (x+7) + (2x+5) + (x+10)}{5}10=5x+(x+4)+(x+7)+(2x+5)+(x+10)​
Simplify the numerator: 10=x+x+4+x+7+2x+5+x+10510 = \frac{x + x + 4 + x + 7 + 2x + 5 + x + 10}{5}10=5x+x+4+x+7+2x+5+x+10​ 10=6x+26510 = \frac{6x + 26}{5}10=56x+26​
Solve for xxx: 6x+26=506x + 26 = 506x+26=50 6x=246x = 246x=24 x=4x = 4x=4
Step 2: Calculate the last four scores The last four scores are: x+4,x+7,2x+5,x+10x+4, x+7, 2x+5, x+10x+4,x+7,2x+5,x+10.
Substitute x=4x = 4x=4:
· x+4=4+4=8x+4 = 4+4 = 8x+4=4+4=8
· x+7=4+7=11x+7 = 4+7 = 11x+7=4+7=11
· 2x+5=2(4)+5=132x+5 = 2(4)+5 = 132x+5=2(4)+5=13
· x+10=4+10=14x+10 = 4+10 = 14x+10=4+10=14
Step 3: Calculate the mean of the last four scores The mean of 8,11,13,148, 11, 13, 148,11,13,14 is:
Mean=8+11+13+144\text{Mean} = \frac{8 + 11 + 13 + 14}{4}Mean=48+11+13+14​ Mean=464=11.5\text{Mean} = \frac{46}{4} = 11.5Mean=446​=11.5
Correct Answer: (d) 11.5 Verification The five scores are: 4,8,11,13,144, 8, 11, 13, 144,8,11,13,14. The mean of the first score is 444, and the last four scores' mean is 11.511.511.5, which aligns with the solution.