Question

Which of the following is true?

Answer 1

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:

$Mean=\frac{\sum x}{n}$

$Mean_1=\frac{1+1+1+1+1+2+2+2+2+2+2+2+2+3+3+3+4+4+7}{19}\apprxo 2.368$

$Mean_2=\frac{1+1+1+1+1+2+2+2+2+2+2+2+2+3+3+3+4+4}{18}\apprxo 2.111$

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)

$Q_1=1,Q_3=3$

$IQR_1=Q_3-Q_1=3-1=2$

Set 2: (1,1,1,1),1,(2,2,2,2),(2,2,2,2),3,(3,3,4,4)

$Q_1=1,Q_3=3$

$IQR_2=Q_3-Q_1=3-1=2$

The data sets have the same IQR. Option 6 is correct.

Therefore the correct options are 1, 4 and 6.

Answer 2

The first one is correct because that one shows how many times you drank milk today but the rest show how many times you drank milk yesterday.