Answer:
The correct options are 1, 4 and 6.
Step-by-step explanation:
From the given dot plots it is clear that the data set are:
Set 1: 1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,4,4,7
Set 2: 1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,4,4
Formula for mean:
[tex]Mean=\frac{\sum x}{n}[/tex]
[tex]Mean_1=\frac{1+1+1+1+1+2+2+2+2+2+2+2+2+3+3+3+4+4+7}{19}\apprxo 2.368[/tex]
[tex]Mean_2=\frac{1+1+1+1+1+2+2+2+2+2+2+2+2+3+3+3+4+4}{18}\apprxo 2.111[/tex]
Mean of data set 1 is greater than mean of data set 2. Therefore option 1 is correct.
Set 1: (1,1,1,1,1,2,2,2,2),2,(2,2,2,3,3,3,4,4,7)
Set 2: (1,1,1,1,1,2,2,2,2),(2,2,2,2,3,3,3,4,4)
Median of both data sets is 2. Therefore option 4 is correct.
All data values of set 1 and set 2 are same except one value of data set 1, i.e. 7. The data set 1 is more spread than data set 2, therefore the standard deviation of data set 1 is greater. Option 5 is incorrect.
Set 1: (1,1,1,1),1,(2,2,2,2),2,(2,2,2,3),3,(3,4,4,7)
[tex]Q_1=1,Q_3=3[/tex]
[tex]IQR_1=Q_3-Q_1=3-1=2[/tex]
Set 2: (1,1,1,1),1,(2,2,2,2),(2,2,2,2),3,(3,3,4,4)
[tex]Q_1=1,Q_3=3[/tex]
[tex]IQR_2=Q_3-Q_1=3-1=2[/tex]
The data sets have the same IQR. Option 6 is correct.
Therefore the correct options are 1, 4 and 6.
