Jorge asked 15 of his classmates how many states in the U.S. they have been to. The results are shown in the dot plot. Which of the following statements is true? Four out of 5 stud... Jorge asked 15 of his classmates how many states in the U.S. they have been to. The results are shown in the dot plot. Which of the following statements is true? Four out of 5 students have been to only 1 or 2 states. The mode of this data set is 5. The median number of states the students have been to is 3. One student has been to 7 states. Read more

Steps to Solve

1. Counting the Dots for Each Value

   From the dot plot, count the number of dots over each number of states:

   • 1 state: 6 dots
   • 2 states: 4 dots
   • 3 states: 2 dots
   • 4 states: 1 dot
   • 5 states: 1 dot

2. Finding the Mode

   The mode is the number that appears most frequently. In this case:

   • The number with the most dots is 1 state (6 dots).
   • Therefore, the mode is 1.

3. Finding the Median

   To find the median, first list out all the numbers of states in order based on the dot counts: $$ 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 5 $$

   The total number of responses is 15 (an odd number). To find the median, locate the middle value (the 8th value):

   • The 8th value in the ordered list is 2.
   • Therefore, the median is 2.

4. Evaluating the Statements

   Now, evaluate the truth of each statement:

   • Statement 1: Four out of 5 students have been to only 1 or 2 states. (False, since 6 have been to 1 and 4 to 2)
   • Statement 2: The mode of this data set is 5. (False, the mode is 1)
   • Statement 3: The median number of states the students have been to is 3. (False, the median is 2)
   • Statement 4: One student has been to 7 states. (False, there’s no mention of 7 states in the dot plot)

5. Conclusion

   All presented statements are false.