Standard Deviation

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

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 values2. Find your Mean3. 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 Deviation1. To calculate the Standard Deviation, take the

square root of the Variance

Mean =

600 + 470 + 170 + 430 + 300

=

1970

= 3945 5

Now, we calculate each dogs difference from the Mean:

To calculate the Variance, take each difference, square it, and then average the result:

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 = 147.32... = 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.Rottweilers are tall dogs. And Dachshunds are a bit short

Steps:1. Write down your values2. Find your Mean3. Find your Variance

1. To calculate the Variance, take each difference, square them, and then average the results.

4. Find your Standard Deviation1. 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 Diet Unhealthy Diet

750N 800N

695N 850N

720N 795N

755N 800N

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

750N 800N

695N 850N

720N 795N

755N 800N

1. Values2. Mean3. Find your Variance4. Find your Standard Deviation5. Use “n-1” instead of “n”

Standard Deviation

Unit Test 11. Parts of scientific method2. Characteristics of living things (all 8 and what they

mean)3. Designing your own experiment (including graphing

and labeling)4. Standard Deviation Calculation5. 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)

335 175

290 160

270 190

250 200

280 210

275 220

400 230

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 method2. Characteristics of living things (all 8 and what they mean)3. Designing your own experiment (including graphing and labeling)4. Standard Deviation Calculation5. What is science used for?