Construct a modified boxplot for the data.

The weight in ounces of 27 tomatoes are listed below. Construct a modified boxplot for the data.

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

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.

60

step-by-step explanation: