Question

Let \( x \) be the median of the data: 13, 17, 52, 56, 65, 35, 77, 39, 15, 37. If 35 is replaced by 53 in the data, then the median of the new data will be \( y \). What is the difference between \( x \) and \( y \)?

• A. 6.5
• B. 7.5
• C. 8
• D. 9

Hint:

When calculating the median, ensure the data is sorted, and the median is the middle number (or average of the two middle numbers) if the data set has an odd number of elements.

Answer 1

The Correct Option is A

The data is: 13, 17, 52, 56, 65, 35, 77, 39, 15, 37. First, sort the data: \[ 13, 15, 17, 35, 37, 39, 52, 56, 65, 77 \] The median \( x \) is the average of the 5th and 6th terms: \[ x = \frac{37 + 39}{2} = 38 \] Now, replace 35 with 53: \[ 13, 15, 17, 39, 37, 52, 53, 56, 65, 77 \] The new median \( y \) is the average of the 5th and 6th terms: \[ y = \frac{37 + 39}{2} = 38 \] The difference between \( x \) and \( y \) is: \[ \boxed{6.5} \]