Standard Deviation

Used to find out if a value is significantly different than the average. For instance: Was a larger bubble caused by adding food coloring, or was it just due to random variation in blowing? Use the Standard Deviation formula to find out if a value is different enough from the average.

Standard Deviation

Example You and your friends have just measured the heights of your dogs (in millimeters): Find out the Average (Mean), the Variance, and the Standard Deviation. Your first step is to find the Mean:

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

Steps: 1.Write down your values 2.Find your Mean 3.Find your Variance 1.To calculate the Variance, take the differences b/w the values and the average, square them, and then average the results. 4.Find your Standard Deviation 1.To calculate the Standard Deviation, take the square root of the Variance

Mean = = 1970 =

Now, we calculate each dogs difference from the Mean: To calculate the Variance, take each difference, square it, and then average the result:

And the Standard Deviation is just the square root of Variance, so: Standard Deviation: σ = √21,704 = = 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. Rottweilers are tall dogs. And Dachshunds are a bit short

Steps: 1.Write down your values 2.Find your Mean 3.Find your Variance 1.To calculate the Variance, take each difference, square them, and then average the results. 4.Find your Standard Deviation 1.To calculate the Standard Deviation, take the square root of the Variance 5.Use “n-1” when you calculate your variance – our example just used “n” 1.So if we have 10 data points, n = 10 and n-1 = 9.

Class Practice (follow with whiteboards) Healthy DietUnhealthy Diet 750N800N 695N850N 720N795N 755N800N Class Practice – 7 people, measuring their weight – is there a significant difference between the weights of people who eat a balanced diet and those who don’t? (all men at age 40, units in Newtons, metric unit for weight)

Healthy Diet Unhealthy Diet 750N800N 695N850N 720N795N 755N800N 1.Values 2.Mean 3.Find your Variance 4.Find your Standard Deviation 5.Use “n-1” instead of “n”

Standard Deviation

Unit Test 1 1.Parts of scientific method 2.Characteristics of living things (all 8 and what they mean) 3.Designing your own experiment (including graphing and labeling) 4.Standard Deviation Calculation 5.What is science used for? Studying: Review your notes, memorize the 8 characteristics of life. Make sure you can calculate standard deviation.

1 mile from the plant (ppm)10 mile from the plant (ppm) Example SD problem: A group of scientists studying the effect of pollution on the environment measured water quality along a river 1 mile from a waste treatment plant, and along the same river 10 miles from the same plant. The concentration of pollution in the river is measured in parts per million, or ppm. When the scientists publish their results, they claim that the river contains a higher concentration of pollutants near the plant. Is that true? 1.Parts of scientific method 2.Characteristics of living things (all 8 and what they mean) 3.Designing your own experiment (including graphing and labeling) 4.Standard Deviation Calculation 5.What is science used for?