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Statistics in Biology: Mean & Standard Deviation

Statistics in Biology: Mean & Standard Deviation. Essential Question: How are statistics used to interpret data and determine the accuracy of experimental results?. Statistics. The science of collection, presentation, analysis, and interpretation of data

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Statistics in Biology: Mean & Standard Deviation

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  1. Statistics in Biology: Mean & Standard Deviation Essential Question: How are statistics used to interpret data and determine the accuracy of experimental results?

  2. Statistics • The science of collection, presentation, analysis, and interpretation of data • Statistical analysis allows us to poll a small sample of the larger population and make inferences of what is occurring in that population

  3. Most data is represented in bar graphs known as histograms

  4. Both histograms to the left form a “bell curve” • The bell curve is called a normal distribution. • Typical data will show a normal distribution

  5. Both histograms have the same mean (average) of five but they differ in their variation or range of values. • Histogram 1 has a range of 8 units and Histogram 2 has a range of 4 units. • There is more variation in histogram 1.

  6. Measures of Variability in Data • Two ways to describe variation in data is range & standard deviation • Standard deviation is a measure of how far data points deviate (vary) from the mean • Which histogram has the higher standard deviation??

  7. Calculating Standard Deviation

  8. Video on Calculating Standard Deviation

  9. Calculating Standard Deviation

  10. Calculate the Standard Deviation from the Video Data Set • Mean = 3.6; Standard deviation = 2.7 Sample Data Set: 0, 2, 4, 5, 7

  11. Practice Calculating Standard Deviation

  12. Practice Calculating Standard Deviation

  13. Understanding Two Different Standard Deviations • The standard deviations for the two histograms are different. • s=2.053 for histogram #1 • s=1.046 for histogram #2 • This makes sense because histogram #1 has more deviation or variation from the mean of 5.

  14. Interesting Facts About Standard Deviations and Normal Distributions • In a normal distribution, 68% of the data points will fall within plus or minus 1 standard deviation. • The percentage of individuals falling within plus or minus 2 standard deviations is 95%. • 3 standard deviations is 99%. • This is often called the 68-95-99% rule.

  15. Describing Variation Using Standard Deviation • 68% of all data fall within ± 1 standard deviation of the mean • 95% of all data fall within ± 2 standard deviations of the mean • 98%of all data fall within± 3 standard deviations of the mean

  16. Standard Deviation

  17. In histogram 1- 68% of all the data points fall between 2.947 and 7.053. 95% of all the data points fall between 9.106 and 0.894. In histogram 2- 68% of all the data points fall between 6.046 and 3.954. 95% of all the data points fall between 7.092 and 2.908

  18. Figure it out with a Partner!! A student was measuring the height of mung beans. The height of 200 plants was measured. The mean height of the mung beans was 4 cm and the standard deviation was .5 cm. 1) What percentage of the plants had a height of 4 and 4.5 cm? 2) What percentage of the plants had a height between 3 and 4 cm?

  19. Figure it out with a Partner!! A student is germinating lettuce seeds in a petri dish and after three days, 95% of them are between 1.1 cm and 1.7 cm long. Assuming that the data is normally distributed determine the mean and the standard deviation.

  20. Figure it out with a Partner!! A student is measuring the mass of pill bugs and finds that 99.7% falls between .034 g and 0.18 g. Assuming that the data is normally distributed, determine the mean and standard deviation.

  21. Standard Deviation…what the numbers mean

  22. Practice Calculating Standard Deviation Using YOUR data Determine the standard deviation, s, for the bean lab.

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