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

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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?

- 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)

- 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

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
- 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

- 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:

- 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

- To calculate the Variance, take each difference, square it, and then average the result:
- So, the Variance is 21,704.

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:

- So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what is extra large or extra small.
- Rottweilersare tall dogs. And Dachshunds are a bit short ... but don't tell them!

- 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?

- To find out calculate the standard deviation for each of your data sets, and then put them on the graph.
- Ex. My fake standard deviations are 2.3cm for Gatorade, and 1.2cm for Water. I put them on the graph as little lines at the tops of the bars

- Notice the error bars overlap between my two sets of fake data…
- This means that the difference between my results isn’t significant enough (in other words, they might as well not be different, so my experiment proves nothing!)

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