Using Excel To Generate Probability Distribution For A Binomial Random Variable And Analyzing Data On Household Size And Computer Usage In The US
- Mean and median
Mean = sum of data points/ sample size (n) = 75/30 = 2.50
Median
Sort the data in ascending order
Sample size = 30 (even number)
The mean and median are representative of the central tendency of the given data and highlights the average number of people in a household. Considering that the data may contain outliers in the form of household with 6 and 8 members, it would be appropriate to use median instead of mean as the mean may be influenced by extreme values which is not the case for median.
- Variance and standard deviation
Standard deviation
The above statistics reveal the dispersion in the data and the deviation of the data points from the average value.
Percentage of US households has fax machine = 10%
Percentage of US households has personal computer= 52%
Percentage of US households has fax machine and has personal computer P(PC| Fax) =91%
Joint probability table can be formed based on the above shown probabilities
|
US household has fax /PC |
Fax yes |
Fax no |
Total |
|
PC yes |
0.091 |
0.429 |
0.52 |
|
PC no |
0.009 |
0.471 |
0.48 |
|
Total |
0.10 |
0.90 |
1.0 |
- Probability that a randomly selected US household would has a fax machine and a personal computer
- Probability that a randomly selected US household would has a fax machine or a personal computer
- Probability that a randomly selected US household would has a fax machine and does not have a personal computer
- Probability that a randomly selected US household would has neither a fax machine nor a personal computer.