Probability and counting rules; Discrete probability distributions

profileislandbuilt
Forum2.xlsx

Sheet1

Type Year Make Model Price MPG(CITY) MPG (HIGHWAY) Weight
variable type: qualitative variable type: quantitative variable type: qualitative variable type: qualitative variable type: quantitative variable type: quantitative variable type: quantitative variable type: quantitative
SUV 2021 Mazda CX-30 $22,795 25 33 3232
compact crossover 2021 Toyota rav4prime $29,458 36 40 5,530
SUV 2021 Chrysler Voyager $28,730 19 28 4,330
minivan 2020 kia Sedona $28,720 18 24 6,085
minivan 2020 Dodge grand caravan $29,025 17 25 4,510
passenger wagon 2020 Ford transit connect $28,315 24 26 3,689
SUV 2020 Volkswagen Tigwan $25,965 22 29 3,847
SUV 2019 kia Sorento $28,110 22 29 3,810
SUV 2020 Honda Odyssey $32,110 19 28 4,593
SUV 2021 Hyundai Palisade $33,665 19 24 4,284
sports car 2020 Bugatti La Voiture $3,250,000 9 14 4,400
SUMMARY BEFORE ADDING OUTLIER
mean $28,689 $22 $29 $4,391
standard deviation 2977.7926966873 5.5467708324 4.8579831206 863.2415652643
median $28,725 $21 $28 $4,307
SUMMARY AFTER ADDING OUTLIER
mean $321,536 $21 $27 $4,392
standard deviation $971,266 $7 $6 $819
median $28,730 $19 $28 $4,330
DISCUSSION
From the initial analysis, the following can be established: The average MPG stands at 22 in the city and at 14 on the highway. This defines the average of all the vehicles selected in the list. Therefore, this figure can be used as a substitute for all the MPG figures respectively. However, the MPG figure for the highway deviates from the central measure of tendency with a certain value. This measure of dispersion is determined by the standard deviation. In the MPG in the city, the standard deviation is given by 5.55. this figure is used in determining the range within which most of the data points are found, defined from the central point of tendency (Mean). This is given by 16.55 and 2755. Therefore, the city MPG for all the data points is within the given range at a confidence interval of 95%. the same concept can be applied in the subsequent means and standard deviation. The median point defines the central position of the data points, when they are arranged in a chronological manner. After addition of the outlier [chosen one is Bugatti. The figures change tremendously. The figures chosen for descriptive statistics, hike up for the standard deviation, but reduces for the mean and the media. An increase in the measures of dispersion is attributed with a decrease in the values for measures of central tendency. This is because larger outliers are attributed to minimizing the measures of central tendency, and hence the deviation from these points is increased.

Without supercar

Without supercar
Mean 28689.3
Standard Error 941.6607321347
Median 28725
Mode ERROR:#N/A
Standard Deviation 2977.7926966873
Sample Variance 8867249.34444445
Kurtosis 1.2469446572
Skewness -0.3237289483
Range 10870
Minimum 22795
Maximum 33665
Sum 286893
Count 10
Confidence Level(95.0%) 2130.1845701243

With Supercar

With Supercar
Mean 321535.727272727
Standard Error 292847.665977757
Median 28730
Mode ERROR:#N/A
Standard Deviation 971265.828779546
Sample Variance 943357310154.818
Kurtosis 10.9997518649
Skewness 3.3165733432
Range 3227205
Minimum 22795
Maximum 3250000
Sum 3536893
Count 11
Confidence Level(95.0%) 652505.262278539