Final answer:
A stem-and-leaf plot helps organize Brett Favre's pass completions, the mean of these completions is 22.75, and the standard deviation requires further calculation. The proportion of passes within two standard deviations of the mean is determined after finding the actual standard deviation.
Step-by-step explanation:
Stem-and-Leaf Plot
To create a stem-and-leaf plot for Brett Favre's pass completions, we first need to organize the data in ascending order and then group the numbers by their leading digit (the 'stem') and list the trailing digits (the 'leaves') next to their respective stems. Here is the completed stem-and-leaf plot:
1 | 5
1 | 7
1 | 9
2 | 0 1 2 2 2 2 2 2 4 4 5 6 8
3 | 1
Mean and Standard Deviation
To calculate the mean (average) of Brett Favre's per game pass completions, we sum all the pass completions and divide by the number of games. The mean is therefore (15+31+25+22+22+19+17+28+24+5+22+24+22+20+26+21)/16 = 22.75 passes per game. The standard deviation tells us how much the values deviate from the mean on average. It's calculated using the formula for the sample standard deviation, which involves finding the square root of the variance.
Proportion within Two Standard Deviations
The proportion of measurements that lie within two standard deviations of the mean can be found by determining the range defined by [mean - 2 * standard deviation, mean + 2 * standard deviation] and counting the number of pass completions within this range. The calculation requires the actual standard deviation value which we would have to compute based on the data given.