Question

1. the student who traveled to 5 states visited 5 new states during a vacation. does increasing the 5 to 10 change the median? if so, how? select the correct choice below and, if necessary, fill in the answer box within your choice.

a. yes. it decreases to

b. no. it stays the same.
c. yes. it increases to

Explanation:

Step1: Recall Median Definition

The median is the middle value (or average of two middle values) in a sorted dataset. When a data point changes, we check if the middle position's value is affected.

Step2: Analyze the Change

Original value: 5 states. New value: 10 states. To determine median change, we need the full dataset, but typically, changing one value (especially if it's not the middle one) might not affect the median. However, if we assume the dataset was sorted, and the student's value was part of the data, increasing 5 to 10—if the median was based on the middle of other values or if this value was not the median position, the median might stay the same. But wait, maybe the original dataset had an odd number of values. Wait, the key here: when you change a value from 5 to 10, if the median was the middle value, and this value was not the median (e.g., in a dataset where median is the middle, and 5 was below or above the median), changing it to 10—if the median is the middle of the sorted data, and the number of data points doesn't change (just one value is updated), the median position (n/2 or (n+1)/2) remains the same. So the median stays the same. So the correct choice is B.

Answer:

B. No. It stays the same.