1. How to describe a graph Otherwise called CUSS
Do after Features of Distributions Activity

2. 4. Spread discuss the variability of the data (how spread out it is)
Range, IQR, standard deviation
Pick the variability measurement that makes most sense. (ie Sometimes IQR means more than range)

3. Variability

4. Why is the study of variability important?
Allows us to distinguish between usual & unusual values
In some situations, want more/less variability
scores on standardized tests
time bombs
medicine

5. Measures of Variability
range (max-min)
interquartile range (Q3-Q1)
deviations
variance
standard deviation
Lower case Greek letter sigma

6. Suppose that we have these data values:
Find the mean. = 28
Find the deviations.
What is the sum of the deviations from the mean?

7.
Square the deviations:
Find the average of the squared deviations:

8. The average of the deviations squared is called the variance.
parameter
statistic
Population Sample

9. Calculation of variance of population

10. Calculation of variance of a sampledf

11. A standard deviation is a measure of the average deviation from the mean.

12. Calculation of standard deviation for population

13. Calculation of standard deviation for a sample

14. Degrees of Freedom (df)
n deviations contain (n - 1) independent pieces of information about variability

15. Which measure(s) of variability is/are resistant?
IQR

16. Linear transformation rule
When multiplying or adding a constant to a random variable, the mean changes by both.
When multiplying or adding a constant to a random variable, the standard deviation changes only by multiplication.
Formulas:

17. An appliance repair shop charges a $30 service call to go to a home for a repair. It also charges $25 per hour for labor. From past history, the average length of repairs is 1 hour 15 minutes (1.25 hours) with standard deviation of 20 minutes (1/3 hour). Including the charge for the service call, what is the mean and standard deviation for the charges for labor?
Labor Charge = (x), x= time of repair

18. Rules for Combining two variables
To find the mean for the sum (or difference), add (or subtract) the two means
To find the standard deviation of the sum (or differences), ALWAYS add the variances, then take the square root.
Formulas:
If variables are independent

19. Bicycles arrive at a bike shop in boxes
Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the times for each setup phase are independent with the following means & standard deviations (in minutes). What are the mean and standard deviation for the total bicycle setup times?
Phase
Mean SD
Unpacking
3.5
0.7
Assembly
21.8
2.4
Tuning
12.3
2.7