Scenario

A survey is done about the weight of backpacks of 15 different students. The weight of these backpacks is recorded in pounds. Our goal is to analyze these weights by computing a 5-number-summary, and sketching a histogram and a boxplot.

The Data

Here, we record the weight of the 15 backpacks:

BackpackWeight <- c(17,18,19,20,9,10,13,14,25,15,16,21,11,12,22)

Again, these weights are all in pounds.

The 5 Number Summary

Using R commands, we compute the minimum, 1st quartile, median, 3rd quartile, and maximum values of this data set.

min(BackpackWeight) #this calculates the minimum value
## [1] 9
max(BackpackWeight) #this calculates the maximum value
## [1] 25
median(BackpackWeight) #this calculates the median
## [1] 16
quantile(BackpackWeight, 0.5) #another way to calculate the median
## 50% 
##  16
quantile(BackpackWeight, 0.25) #first quartile
##  25% 
## 12.5
quantile(BackpackWeight, 0.75) #third quartile
##  75% 
## 19.5
quantile(BackpackWeight, c(0, 0.25, 0.5, 0.75, 1)) #the full 5-number summary
##   0%  25%  50%  75% 100% 
##  9.0 12.5 16.0 19.5 25.0

Boxplot and Histogram

Finally, to display this data, we construct a histogram and a boxplot.

BackpackDataSet <- data.frame(BackpackWeight = BackpackWeight)
ggplot(BackpackDataSet, aes(x=BackpackWeight))+
  geom_boxplot(col="darkgreen", fill="green")

ggplot(BackpackDataSet, aes(x=BackpackWeight))+
  geom_histogram(binwidth=2, col="blue", fill="lightblue")

In Conclusion

This data set is quite small, but it gives us a look at how we can record quantitative data (i.e., a list of numbers), and summarize this data by using a 5-number summary and various data displays.