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.
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.
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.
Since both data set's IQR is 2, therefore, 6th statement is true.