Respuesta :
Answer:
See explanation below and figure attached.
Step-by-step explanation:
We can construct the boxplot with the following steps:
Data given:
We can follow these steps in order to construct the boxplot required
1) Order the data set
1.7 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6
2.6 2.6 2.7 2.7 2.7 2.8 2.8 2.8 2.9
2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2
2) Calculate the median
The median for this case would be the position 14 since we have 27 values
Median= 2.7
3) Calculate Q1
Data values below 2.7 are: 1.7 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6 2.6 2.6. Their median is at the middle: Q1 = 2.5
4) Calculate Q3
Data values above 2.7 are: 2.8 2.8 2.8 2.9 2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2. Their median is at the middle: Q3 = 2.95
5) Calculate max and min
Max = 4.2 , Min = 1.7
6) Calculate IQR
IQR= Q3-Q1= 2.95-2.5=0.45
7) Minimum and maximum value for the boxplot
MWB= Q1-1.5 IQR= 2.5-1.5*0.45=1.825
UWB= Q3+1.5 IQR= 2.5+1.5*0.45=3.175
8) Identify outliers
Values higher than UWB and lower than MWB are possible outliers
And we can construct the boxplot with the following R code:
> x<-c(1.7, 2.0, 2.2, 2.2, 2.4, 2.5, 2.5, 2.5, 2.6,
+ 2.6, 2.6, 2.7, 2.7, 2.7, 2.8, 2.8, 2.8, 2.9,
+ 2.9, 2.9, 3.0, 3.0, 3.1, 3.1, 3.3, 3.6, 4.2)
> summary(x)
Min. 1st Qu. Median Mean 3rd Qu. Max.
1.700 2.500 2.700 2.752 2.950 4.200
> length(x)
[1] 27
> boxplot(x,main="Boxplot of data")
And as we can see we have the following picture attached for the boxplot.
