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

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