Question

On a 10 item test, three students in prof. miller's advanced chemistry seminar received scores of two, five, and eight, respectively. for this distribution of test scores, standard deviation is equal to the square root of

Answer 1

Your set is 2, 5 and 8.

In order to calculate the standard deviation, first, you need to calculate the mean of the scores:
m = (2 + 5 + 8) / 3
    = 15 / 3
    = 5

Then, find the variance: subtract the mean from each value, square the results, sum them up and divide it by the number of scores.
(2 - 5)² = 9
(5 - 5)² = 0
(8 - 5)² = 9
Therefore:
v = (9 + 0 + 9) / 3 
   = 18 / 3
   = 6

The standard deviation is the square root of the variance:
σ = √6 
   = 2.45

In conclusion, the standard deviation can be calculated by the formula:
$\sigma = \sqrt{ \frac{\sum(v - m)^{2} }{n} }$