Answer:
1st, 4th and 6th statements are true.
Step-by-step explanation:
We have been given two dot-plots and we are asked to select all the true statements about given dot plots.
Let us write all the data points of both dot plots.
Data set 1:
1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 7.
Data set 2:
1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4.
1. The mean of data set 1 is greater than the mean of data set 2.
Let us find mean of both data sets.
![\text{Mean of data set 1}=\frac{1+1+1+1+1+2+2+2+2+2+2+2+2+3+3+3+4+4+7}{19}](https://tex.z-dn.net/?f=%5Ctext%7BMean%20of%20data%20set%201%7D%3D%5Cfrac%7B1%2B1%2B1%2B1%2B1%2B2%2B2%2B2%2B2%2B2%2B2%2B2%2B2%2B3%2B3%2B3%2B4%2B4%2B7%7D%7B19%7D)
![\text{Mean of data set 1}=\frac{45}{19}](https://tex.z-dn.net/?f=%5Ctext%7BMean%20of%20data%20set%201%7D%3D%5Cfrac%7B45%7D%7B19%7D)
![\text{Mean of data set 2}=\frac{1+1+1+1+1+2+2+2+2+2+2+2+2+3+3+3+4+4}{18}](https://tex.z-dn.net/?f=%5Ctext%7BMean%20of%20data%20set%202%7D%3D%5Cfrac%7B1%2B1%2B1%2B1%2B1%2B2%2B2%2B2%2B2%2B2%2B2%2B2%2B2%2B3%2B3%2B3%2B4%2B4%7D%7B18%7D)
![\text{Mean of data set 2}=\frac{38}{18}](https://tex.z-dn.net/?f=%5Ctext%7BMean%20of%20data%20set%202%7D%3D%5Cfrac%7B38%7D%7B18%7D)
![\text{Mean of data set 2}=2.11](https://tex.z-dn.net/?f=%5Ctext%7BMean%20of%20data%20set%202%7D%3D2.11)
We can see that mean of data set 1 is greater than mean of data set 2, therefore, 1st statement is true.
2. The mean of data set 1 is equal to the mean of data set 2.
Since mean of data set 1 is greater than mean of data set 2, therefore, 2nd statement is false.
3. The median of data set 1 is greater than the median of data set 2.
Since data set 1 has 19 data points, so median of data set 1 will be value of 10th data set, that is 2.
Our data set 2 has 18 data points, so median of data set 2 will be the average of 9th and 10th data points.
![\text{Median of data set 2}=\frac{2+2}{2}](https://tex.z-dn.net/?f=%5Ctext%7BMedian%20of%20data%20set%202%7D%3D%5Cfrac%7B2%2B2%7D%7B2%7D)
Since median of data set 2 is also 2, therefore, 3rd statement is not true.
4. The median of data set 1 is equal to the median of data set 2.
Since both data set's median is 2, therefore, 4th statement is true.
5. The standard deviation of data set 1 is smaller than the standard deviation of data set 2.
Using online SD calculator we get SD of data set 1 is 1.422 and SD of data set 2 is 0.936. Since 1.422 is greater than 0.936, therefore, 5th statement is false.
6. The data sets have the same interquartile range.
![Q_1\text{ of data set 1}=1](https://tex.z-dn.net/?f=Q_1%5Ctext%7B%20of%20data%20set%201%7D%3D1)
![\text{IQR of data set 1}=3-1=2](https://tex.z-dn.net/?f=%5Ctext%7BIQR%20of%20data%20set%201%7D%3D3-1%3D2)
![Q_1\text{ of data set 2}=1](https://tex.z-dn.net/?f=Q_1%5Ctext%7B%20of%20data%20set%202%7D%3D1)
![Q_3\text{ of data set 2}=3](https://tex.z-dn.net/?f=Q_3%5Ctext%7B%20of%20data%20set%202%7D%3D3)
![\text{IQR of data set 2}=3-1=2](https://tex.z-dn.net/?f=%5Ctext%7BIQR%20of%20data%20set%202%7D%3D3-1%3D2)
Since both data set's IQR is 2, therefore, 6th statement is true.