Jianing Min's MATH 6820 Blog

As required in the instruction, I find the data set, remove all the missing data, and randomly pick 1oo sample from the above data set. Since my first name’s first letter is between A to J, I look at the haircut prices of the men and women in the class. (The relevant variables in the data frame are Haircut and Gender.)

1. Construct parallel stripcharts of the variable by gender.

From the parallel stripchart we can compare the distribution of two groups of students and see that male students’haircut prices have narrow range, which is from 0 to 25 dollars. However, female students’ haircut prices have very wide range, which is from 0 to 145.On one hand, there are one third of male students(11) do not spend any money on haircut and almost half of male students(16) spend from $10 to $15, and only two male students spend more than $20 on haircut. The maximum money spend spends on haircut for male student is $25. On the other hand, over two third (47) of female students spend from $10 to $50 on haircut. Three females do not spend any money on haircut and only 4 female students spend more than $100. The maximum money spends on haircut for female student is $146. The distributions of these two groups are quite different.

2.Construct parallel quantile plots of the male values and of the female values. Write several sentences that help the reader interpret the quantile plots.

From the graph below we can see that the first quartile of male student is $0 , median quartile of male is about $10 and upper quartile is about $15. However, first quartile of female student is about $10, the median quartile of female is about $30 and upper quartile is about $50. Comparing these two groups, we are clear that female students spend more than male students on haircut, no matter for the first quartile or the medium quartile of people. Moreover, the median quartile of female student to have a haircut is more than the upper quartile of male student.

3.Construct a quantile-quantile plot of the male and female values.

From the first graph we can see that the average female student haircut price is obviously higher than male student (the slope of the line is obviously greater than 1). However, the “extra price” is not constant. We have to observe the graph in different segments. If the male student haircut price is within the low price region, saying $0-$10, female haircut price is about $10 higher. However, if the male student haircut price is more than $10, female haircut price will increase faster than the low price region. For the high price region (for male haircut), say $10-$24, for every one dollar more increase for male haircut, female haircut price will increase 5 dollar more (from $25 to $90). For the high price region (for male haircut), saying $25 and more, female price increase rapidly, ranging from $110 to $145.  Meanwhile, there are also points located at y=x line, which means several female spend nothing as male spend.

4. Construct a Tukey m-d plot from the quantiles of the two samples.  Interpret the plot.  Is there a simple relationship between the male values and the female values?

For the mean price between $0 and $20, the difference has a range from $0 to $20 and the difference rise and fall, quite fluctuating. For the mean price more than $20, the differences continue growing, with a slope almost equal to 1.5. The graph also indicates that the biggest difference is about $120 and the smallest difference is $0. There are no simple relationship between male haircut price and female haircut price.

In sum, for the mean price within $0 to $20, the difference is quite fluctuating. However, for the mean price over $20, it seems we can interpret the line as linear relationship, y=-10+1.5x (y is the price difference and x is the mean price.) Female haircut price is always expansive than male haircut price, except those haircut by themselves, relatives or friends with no charge. This conclusion is easy to understand. For simple haircut at a small hair salon, the price difference is not that big. However, if a female want to have a perm or color hair at a high class salon, the price will surely high. Meanwhile, males do not tend to decorate their hair as females, so they spend less than female.

This entry was posted on Friday, February 22nd, 2013 at 8:02 pm and is filed under Uncategorized and You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.