Question

use the data table to answer 8–11.
states traveled to or lived in
2, 5, 6, 2, 6, 1, 10, 7, 2, 1, 6, 2, 1, 9, 13

1. does increasing the 5 to 10 change the mode? how so? select the correct choice below and, if necessary, fill in the answer box within your choice.

Explanation:

Step1: Find original mode

First, we count the frequency of each number in the original data set: \(2, 5, 6, 2, 6, 1, 10, 7, 2, 1, 6, 2, 1, 9, 13\).

• Count of \(1\): Let's see, the \(1\)s are at positions (6,10,13) → 3 times.
• Count of \(2\): Positions (1,4,9,12) → Wait, let's list all: \(2\) appears at index 0 (2), 3 (2), 8 (2), 11 (2) → Wait, original data: let's list all elements: 2,5,6,2,6,1,10,7,2,1,6,2,1,9,13. So:
• \(1\): occurs at 5th (1), 9th (1), 12th (1) → 3 times.
• \(2\): occurs at 0th (2), 3rd (2), 8th (2), 11th (2) → 4 times.
• \(6\): occurs at 2nd (6), 4th (6), 10th (6) → 3 times.
• Others: 5 (1), 10 (1),7(1),9(1),13(1). So original mode is \(2\) (highest frequency, 4 times).

Step2: Change 5 to 10 and find new mode

Now, change the \(5\) to \(10\). The new data set is: \(2, 10, 6, 2, 6, 1, 10, 7, 2, 1, 6, 2, 1, 9, 13\).
Now count frequencies:

• \(1\): still 3 times (positions 5,9,12).
• \(2\): positions 0,3,8,11 → 4 times.
• \(6\): positions 2,4,10 → 3 times.
• \(10\): positions 1,6 → 2 times.
• Others:7(1),9(1),13(1). So the frequency of \(2\) is still 4, which is the highest. So the mode remains \(2\), so increasing 5 to 10 does not change the mode.

Answer:

No, increasing the 5 to 10 does not change the mode. The mode remains \(2\) (since the frequency of \(2\) is still the highest after the change).