Question

Let \( x \) be the median of the data: 23, 17, 19, 11, 7, 3, 13, 2, 5, 29. Let \( y \) be the median of the same data set obtained by replacing 2 by 21 and 13 by 31. What is the value of \( |x - y| \)?

• A. 6
• B. 6.5
• C. 7
• D. 7.5

Hint:

To find the median, always arrange the data in ascending order and find the middle value (or average of the two middle values).

Answer 1

The Correct Option is C

The original data set is: \[ 23, 17, 19, 11, 7, 3, 13, 2, 5, 29 \] Arranging the data in ascending order: \[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 \] The median \( x \) is the average of the 5th and 6th numbers: \[ x = \frac{11 + 13}{2} = 12 \] Now, replace 2 by 21 and 13 by 31. The modified data set is: \[ 21, 3, 5, 7, 11, 31, 17, 19, 23, 29 \] Arranging this data in ascending order: \[ 3, 5, 7, 11, 17, 19, 21, 23, 29, 31 \] The new median \( y \) is the average of the 5th and 6th numbers: \[ y = \frac{17 + 19}{2} = 18 \] Thus, \( |x - y| = |12 - 18| = 6 \).