1. Understanding and Comparing Distributions
Week 2
Lecture 3 Chapter 4.
Understanding and Comparing Distributions

2. Boxplot of Calories of Donuts By Their Type
Type of Donuts: Yeast, filled, and cake.
This display is for 29 donuts.
There was one donut that belonged to an “other” category; I removed it from the 30 donuts data file (we won’t have a boxplot for one observation!).
StatCrunch:
Graph>boxplot>Select Column(s)>Calories
Group by: Type of donuts
Select: use fences to identify outliers

3. Boxplot of Calories of Donuts
Cake:
Shape: about symmetric
Centre: the median is in almost in the middle of the box of boxplot.
Spread: the width of the box (IQR) is small, from 250 to 280.
Potential outliers: one point is plotted individually at 340.
Filled:
Shape: Right skewed
Centre: the median is not almost in the middle of the box of boxplot
Spread: the width of the box (IQR) is somewhat wide, from 210 to 270.
Potential outliers: one point is plotted individually at 400.
Yeast:
Centre: the median is in not almost in the middle of the box of boxplot,
and it is the lowest of all three types (200 calories)
Spread: the width of the box (IQR) is the widest among the three types of donuts, from 190 to 270.
Potential outliers: no point is plotted individually.

4. Distributions of Calories of Donuts By Their Type
The stem-and-leaf plots for types of donuts:
Variable: Calories for Type of Donut = Cake Decimal point is 2 digit(s) to the right of the colon. Leaf unit = 10
2 :
3 : 04
Variable: Calories for Type of Donut = Filled Decimal point is 2 digit(s) to the right of the colon. Leaf unit = 10
2 :
3 :
4 : 0
Variable: Calories for Type of Donut = Yeast Decimal point is 2 digit(s) to the right of the colon. Leaf unit = 10
1 : 8999
2 : 159
3 : 0

5. Summary Statistics for Calories of Donuts By Their Type
StatCrunch:
stat>summary stat>Select Column(s)>Calories
Group by: Type of donuts
Select any statistics you’d like from the drop down menu

6. Look at all three information for the filled distribution:
the boxplot, summary statistics chart, and the stem-and-leaf plot.
We see that in the boxplot for filled, there is no upper whisker.
The summary statistics chart tells us, what the accurate value for the Q3 is, which is 270, and the max value is 400.
We can see in the boxplot and the stem-and-leaf plot, there is no value between, 270 to 400.
The upper inner fence is: Q IQR = (60) = 360.
This means that we would attempt to draw the upper whisker for filled from Q3 (value of 270) to a number in the data that is close to (less than or equal to) 360. However, we do not have such value in the data, and therefore, we do not have an upper whisker. The last value in this group is for value 400, which is plotted individually.
Variable: Calories for Type of Donut = Filled Decimal point is 2 digit(s) to the right of the colon. Leaf unit = 10
2 :
3 :
4 : 0