What is the standard deviation of the data set given below 2

What is the standard deviation of the data set given below? 2,3,6,9,10 a 3.5 B 10 C 12.5 D.3.5 E 10 F 12.5

Solution

The mean (average) of the numbers 2, 3, 6, 9, 10 is (2+3+6+9+10)/5 = 30/5 = 6.   Now, ( 2- 6)² = 16, (3 – 6)² = 9, (6 -6)² = 0 , ( 9 – 6)² = 9 and ( 10 – 6)² = 16. Also, the mean of the numbers 16, 9, 0, 9 and 16 is (16 + 9 + 0 + 9 + 16) / 5 = 50/5 = 10. Therefore, the standard deviation of the data is 10