Statistics in Biology The Mean Mean ( x ) is a measure of the - - PDF document

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Statistics in Biology

The Mean

Mean (x̄) is a measure of the central tendency

• f a set of data.

(average)

• Ex. Calculate the mean.

Answer = 11.6

The Mean

Graphing the Mean  Bar Graph

Measures of Variability

Range: difference between largest/smallest values in data set Standard deviation (s) is a measure of the spread of most of the data

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Standard Deviation Standard Deviation

68% of all data fall within ± 1 standard deviation of the mean 95% of all data fall within ± 2 standard deviation of the mean 99.7% of all data fall within ± 3 standard deviation of the mean

Standard Deviation Standard Deviation Standard Deviation

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Standard Deviation Standard Deviation Calculating Standard Deviation

1. Calculate the mean 2. Determine the differences 3. Square the differences

• 4. Sum the Squares
• 5. Divide by sample size (n) – 1
• 6. Take the square root

Measurements of Confidence

Uncertainty: the margin of error in a measurement Ex: digital scale: 126.4g (±0.1g)

Standard Error of the Mean

Standard Error of the Mean (SE or SEM): measures how close the sample mean is to the population mean

• Measure of accuracy (if the true mean is known)
• Measure of precision (if the true mean is not known)

The greater the sample size, the less the uncertainty in the calculations

Standard Error (SE or SEM)

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Standard Error Standard Error

95% confidence interval (95% CI): 95% confident that the true means falls between 2 SE above/below calculated mean

Graph with error bars Graph with error bars representing representing SE of the mean 95% confidence interval

Error Bars Error Bars Error Bars

• Look for overlap of error

lines

• If overlap-

difference is NOT significant

• If no overlap-

difference IS significant

Error Bars

Significance of Data

Which graph shows two means that are significantly different? Hint: Look for the non-overlapping error bars. Answer: The means in (c) are statistically different.

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Error Bars

Statements

• Fish2Whale food caused the most growth
• Fish2Whale food caused more fish growth than did Budget Fude

Error Bars

Statements

• More males in all four

regions exhibited the trait measured than did females

• More males in region 3

exhibited the trait measure than did females

The End