Standard DeviationFor UNGROUPED Data

BY: Alvarez, Arcueno, Completo & Tolentino

Deviation (d)

The distance of each observation from the mean

STANDARD DEVIATION (SD)

◦It is the square root of the average of the squared deviation.

FORMULA

Formula with the MeanSD= or

n= total number of observationi = ranges from 1 to n = mean

Example: The Scores of 5 Grade Six students in their Mathematics ExaminationScores Mean d d2

50 74 -24 57679 74 5 2591 74 17 28963 74 -11 12187 74 13 169Total= 370 1180

SD=

= σ(SD)= 15.36

Formula without the meanSD=

= summation of the squares of the scores/data

= square of the summation of the scores

Example: The Scores of 5 Grade Six students in their Mathematics ExaminationScores Mean d d2

50 74 -24 57679 74 5 2591 74 17 28963 74 -11 12187 74 13 169Total= 370 1180

σ=

σ(SD)= 15.36