# Standard Deviation

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Standard Deviation

objective
• Describe standard deviation and it’s importance in biostatistics.

Measure of Dispersion
• Indicates how widely the scores are dispersed around the central point (or mean.)
-Standard deviation

Standard Deviation.
• The most commonly used method of dispersion in oral hygiene.
• The larger the standard deviation, the wider the distribution curve.

Standard Deviation
• SD,  ,  (sigma)
• Indicates how subjects differ from the average of the group/ the more they spread out, the larger the deviation • Based upon ALL scores, not just high/low or middle half
• Analyzes descriptively the spread of scores around the mean
– 14+ 2.51 = Mean of 14 and SD of
2.51

Standard Deviation
• The spread of scores around the mean: • For example, if the mean is 60 and the standard deviation 10, the lowest score might be around 30, and the highest score might be around 90.

Standard Deviation &
Variance
Usefulness
• When comparing the amount of dispersion in two data sets.
• Greater variance = greater dispersion
• Standard deviation--”average” difference between the mean of a sample and each data value in the sample

14+ 2.51 = Mean of 14 and SD of 2.51

Distribution Shape
• Normal
• Skewed
• Multimodial

NORMAL CURVE
• Mean is the focal point from which all assumptions made
• Area under curve = 100%
• Total area divided into segments (these %’s are always the same in the normal curve)
– Between Mean & One SD = 68.26%
– Between Mean & Two SD = 95.45%
– Between Mean & Three SD = 99.7%

Distribution Shape
Skewed

• Most scores are high or low
• Not symmetrical
• Small % of scores are strung out in one direction-away from the majority

“Tail” points to the right = positive skew “Tail” points to the left = negative skew

Shape of Distributions
• Shape of the data is described by its frequency histogram
• Date that behaves normally
– Normal distribution
– Bell shaped curve

Positive Skew

•Positive skew=low scores (tail to right) Low
High
More

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