Problem 1. Consider the following data
Compute the following
The mean
The median
The mode
First, second and third quartiles and the interquartile range
The 20th percentile
Draw the box plot for the given data.
Find the variance and standard deviation assuming that this data is the population (not a sample).
Assuming the variance in part g was 7, how would you modify it if it were instead a sample?
Find the z-scores of 1, 5, 6 and 10 and interpret them. Are there any outliers?
Problem 2. A new test for cancer is reported to be 99% sensitive (when tested with people with cancer, it gives a positive result in 99% of the cases) , and 99% specific (when tested with people without cancer, it gives a negative result in 99% of the cases). Assume that 1% of the population is affected by cancer. Given that a person tested positive for the test, what is the probability that he/she has cancer?
Problem 3. Assume that a factory has three machines A, B, C, each producing an identical product. A is responsible for 10% of the production, B for 30% and C for 60% of the production. 20% of the items produced by A are defective. 10% of items produced by B, and 5% by C. What is the probability that any given defective item was produced by C?