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# Statistics in Science - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Statistics in Science' - makoto

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### Statistics in Science

• 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!!)

• 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

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

• Formula:

Fake tomato plant data(measured after 30 days)

Calculate the mean for each column

• 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

• 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?"

• 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.

• 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 and then average the result

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

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?