1. Lesson: Standard Deviation
Obj: The student will be able to 1) Calculate standard deviation 2) Calculate mean deviation HWK: Worksheet Vocab: 1) standard deviation – a measure of how spread out the numbers are 2) variance – the average of the squared differences from the mean 3) mean deviation – the average of the distances of each value from their mean 4) μ – Greek letter “mu”, used for the mean 5) σ – Greek letter “ sigma”, used for standard deviation

2. a) Find the mean, the variance and the standard deviation.
Ex 1) You and your friends have measured the heights of dogs in your neighborhood (in mm). The heights are (at the shoulders) : 600 mm, 470 mm, 170 mm, 430 mm, and 300 mm
a) Find the mean, the variance and the standard deviation.
Dogs
Heights (mm)
Difference
(x – μ)
Square of differences
(x – μ)²
Rottweiller
Greyhound
Dashshund
Yorkshire
Boston Terrier
Total
Mean (μ)
Variance (mean of squares)
Standard deviation ( σ ) (square root of variance)

3. Ex 2) Which dogs are not within one standard deviation?
Standard deviation is useful. Tells us the heights that are within one standard deviation (147 mm) of the mean.
Ex 2) Which dogs are not within one standard deviation?

4. Ex 3) Sam has scored the following points in the last 20 basketball games. Find the standard deviation. 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4
Scores
(x – μ)
(x – μ)² 9 2 5 4 12 7 8 11 3
Scores
(x – μ)
(x – μ)² 4 12 5 10 9 6
Total
Mean
Variance (mean of squares) σ

5. Ex 4) Find the mean deviation of the following information 3, 6, 6, 7, 8, 11, 15, 16
Number
Distance from the mean
| x – μ | 3 6 7 8 11 15 16
Total μ
Mean deviation (mean of distances)
Mean =
Mean deviation =