Comparing Distributions

About the data:

The data represents a survey of number of shoes for men and women among a random sample of 100 students than have been selected from a large data set of 657 students named “studentdata” from the LearnBayes package contains results from a survey given to a large group of students from a introductory statistics class. We are interested in comparing the number of shoes for male and female students using 4 types go graphs.

Parallel Stripchart:

 

Parallel quantile Plots:

The quartile plot is divided to 3 quantile: first quantile (25th percentile), second quantile -median (50th percentile) and third quantile (75th percentile). Obviously female students tend to have more shoes than males.

The average number of shoes for male is from 1 to 23, while it is from 1 to 100 for female.

The 25th percentile number of shoes for males is 5 shoes, while it is 10 shoes for females.

The 50th percentile or the median  number of shoes for males is 6 shoes, while it is 18 shoes for females.

The 75th percentile number of shoes for males is 7 shoes, while it is 20 shoes for females.

The graph shows that only 20% of females have crazy amounts of shoes (more than 25 shoes) while only 20% of males exceed 10 shoes.

Quantile – Quantile Plot.

The graph shows that all the quantile of the number of shoes for female are are larger than that for males.

Tukey Mean Difference Plot

this graph shows the difference of the quantiles against their average. Again we observe that females have more shoes than males. We can see a linear pattern between quantiles difference and quantiles mean. The graph shows that through the most of the range of the distribution, the females have 20 more shoes than the males.

 

All the four graphs gave comparison between males and females number of shoes distribution, but l think the parallel quantile plot convey more information about the differences between male and female distributions since both are graphed parallely , we have three important points ( including the median) of percentiles of the number of shoes for male and female. also it shows obviously the main theme of the 2 distributions: female have more shoes than the male.

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