Mean and Standard Deviation

[silverflamein]

Bond took four tests and his scores were as shown in the table below. In which test did bond score relatively best among the test takers??
Test - Bond's Score - Mean - Standard Deviation
1 - 86 - 71 - 7
2 - 81 - 70 - 10
3 - 88 - 73 - 8
4 - 78 - 65 - 12


Can somebody show me how to solve this ???

[Anurag@Gurome]

Bond took four tests and his scores were as shown in the table below. In which test did bond score relatively best among the test takers?

Bond has scored relatively best among the test takers in that test in which his score is farthest from the mean in terms of standard deviation.

Say, D is the difference between score and the mean and S is the standard deviation. Then,

• 1. D = (86 - 71) = 15 > 2*7 = 2S
  2. D = (81 - 70) = 11 > 1*10 = S
  3. D = (88 - 73) = 15 < 2*8 = 2S
  4. D = (78 - 65) = 13 > 1*12 = S

Hence, we can see that D is maximum in terms of S for test 1.
Hence, Bond has scored relatively best among the test takers in the 1st test.

[silverflamein]

Thanks alot.....I really appreciate the answer to this question.....