"Concept: The Standard Deviation: The Standard Deviation is the most stable measure of variability. Therefore it is most commonly used in research studies. Calculation of Standard Deviation for Ungrouped Data Standard Deviation for ungrouped data can be computed by the following formula. The formula for Standard Deviation = (sqrt{frac{{∑ X^2}}{N}}) Where x = Deviation from mean of the data, N = Total number of students. Given: Marks of students: 85, 65, 55, 42, 69, 83, 92, 77. Calculation: Mean of the marks = (frac{85~+~65~+~55~+~42~+~69~+~83~+~92~+~77}{8}) (=frac{568}{8}=71) Marks (X) Deviation from the mean (x) = (Marks - Mean) (x2) Square of deviation of the mean 85 85 - 71 = 14 196 65 65 - 71 = -6 36 55 55 - 71 = -16 256 42 42 - 71 = -29 841 69 69 - 71 = 2 4 83 83 - 71 = 12 144 92 92 - 71 = 21 441 77 77 - 71 = 6 36 Total   (sum x^2=1954) We know that, Standard Deviation (SD) = (sqrt{frac{{∑ X^2}}{N}}) Here (sum x^2) = 1954, N = 8 Then, SD = (sqrt{frac{{1954}}{8}}) = (sqrt{244.25}) = 15.63 Thus the standard deviation for this data is 15.63 Additional Information Steps For ungrouped data Add all the scores (∑x) and divide this sum by the number of scores (N) and find out the mean. Find out the difference between scores and means (X - x) and find out deviation (x). Square all the deviation to get x2. Add all the squared deviation to get (sum x^2) Divide (sum x^2) by N. Find out the square root of the obtained values." Answer from Testbook on testbook.com