Question

What is the standard deviation for the data given:
{12, 13, 29, 18, 61, 35, 21}

Answer 1

Standard deviation is 17.1

Answer 2

15.866

Explanation:

you would first find the mean of the data set by adding all the numbers together and dividing by the number of data points given (7 in this case).

• 12+13+29+18+61+35+21 = 189
• 189/7 = 27

you would then use the mean to solve for the standard deviation by using the equation, σ=√Σ(x-μ)²/N.

first, subtract the mean from all the data points

• 12-27=-15, 13-27=-14, 29-27=2, 18-27=-9, 61-27=34, 35-27=8, 21-27=-6

then, square each calculated value from above

• -15²=225, -14²=196, 2²=4, 9²=81, 34²=1156, 8²=64, 6²=36

then, add the squared values together

• 225+196+4+81+1156+64+36 = 1762

you would then divide 1762 by 7 (number of data values given orginally)

• 1762/7 = 251.714

finally, take the square root of 251.714 to find the standard deviation

• 
  `√(251.714) = 15.866`