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. what are the median, mode, and range of the data?

the median is
the mode is
the range is

Explanation:

Step1: Organize the data

First, we need to sort the data in ascending order. The data set is: 1, 1, 1, 2, 2, 2, 2, 5, 6, 6, 6, 7, 9, 10, 13. Let's count the number of data points. There are 15 data points.

Step2: Find the median

The median is the middle value of a sorted data set. For a data set with \( n \) values, if \( n \) is odd, the median is the \( \frac{n + 1}{2} \)-th value. Here, \( n=15 \), so the median is the \( \frac{15+1}{2}=8 \)-th value. Looking at the sorted data: 1, 1, 1, 2, 2, 2, 2, 5, 6, 6, 6, 7, 9, 10, 13. The 8th value is 5. So the median is 5.

Step3: Find the mode

The mode is the value that appears most frequently. Let's count the frequency of each value:

• 1 appears 3 times.
• 2 appears 4 times.
• 5 appears 1 time.
• 6 appears 3 times.
• 7 appears 1 time.
• 9 appears 1 time.
• 10 appears 1 time.
• 13 appears 1 time.

The value 2 appears the most (4 times), so the mode is 2.

Step4: Find the range

The range is the difference between the maximum and minimum values. The minimum value is 1, and the maximum value is 13. So the range is \( 13 - 1 = 12 \).

Answer:

The median is \( \boldsymbol{5} \), the mode is \( \boldsymbol{2} \), the range is \( \boldsymbol{12} \)