Statistics in science
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Statistics in Science. Use multiple samples. In science the more test subjects, the better! (You will get your most accurate results with huge test groups) EX: I am testing the affects of G atorade on the growth of tomato plants:

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Use multiple samples
Use multiple samples

  • In science the more test subjects, the better! (You will get your most accurate results with huge test groups)

  • EX: I am testing the affects of Gatorade on the growth of tomato plants:

    • I DON’T have one plant I water with water and one plant I water with Gatorade

    • I DO have 50 plants I water with water and 50 plants I water with Gatorade (or even more!!)


Why so many samples
Why so many samples?

  • The results on any one specimen could be an accident!

  • Ex: You never know if that one tomato plant would have grown larger than average….just because! (some people are tall, and some people are not)

  • If you have many test subjects, then average their results you get a more accurate representation of what will actually occur


Average also known as mean
Average (also known as mean)

  • To calculate the mean of a group of data simply add all the numbers together, and divide by how many numbers there are

  • Formula:


F ake tomato plant data measured after 30 days
Fake tomato plant data(measured after 30 days)

Calculate the mean for each column



The normal distribution
The normal distribution

  • Data about populations usually can be graphed into a pattern known as the “normal curve”

  • Ex: heights


  • The normal distribution has:

    • Symmetry about the centre point (which is the mean)

    • 50% of the values less than the mean, and 50% greater than the mean


Standard deviation
Standard deviation

  • Standard Deviation

  • The Standard Deviation is a measure of how spread out numbers are.

  • Its symbol is σ (the greek letter sigma)

  • The formula is easy: it is the square root of the Variance. So now you ask, "What is the Variance?"


Variance
Variance

  • The Variance is defined as:

  • The average of the squared differences from the Mean.

  • To calculate the variance follow these steps:

  • Work out the Mean (the simple average of the numbers)

  • Then for each number: subtract the Mean and square the result (the squared difference).

  • Then work out the average of those squared differences.


Example
Example:

  • You and your friends have just measured the heights of your dogs (in millimeters):

  • The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.

  • Find out the Mean, the Variance, and the Standard Deviation.

  • Your first step is to find the Mean:

394 mm




Now do the variance sheet
Now do the variance sheet and then average the result


Standard deviation1
Standard deviation and then average the result

  • Remember our example with the dogs?

  • The mean was 394 mm

  • The variance was 21704

  • But we still needed to calculate the standard deviation!


  • T and then average the resulthe Standard Deviation is just the square root of Variance, so:

  • Standard Deviation: σ = √21,704 = 147.32... = 147 (to the nearest mm)

  • And the good thing about the Standard Deviation is that it is useful. Now we can show which heights are within one Standard Deviation (147mm) of the Mean:



  • 68% knowing what is normal, and what is extra large or extra small. of values are within1 standard deviation of the mean

  • 95% are within 2 standard deviations

  • 99.7% are within 3 standard deviations


  • It is good to know the standard deviation, because we can say that any value is:

  • likely to be within 1 standard deviation (68 out of 100 will be)

  • very likely to be within 2 standard deviations (95 out of 100 will be)

  • almost certainly within 3 standard deviations (997 out of 1000 will be)


Now do the mean variance and standard deviation sheet
Now do the say that any value is:“mean, variance and standard deviation” sheet


Error bars
Error bars say that any value is:

  • Imagine you have made a bar graph to represent your data (such as the one below) How do you know if the difference between your results is enough?





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