Ten randomly selected people were asked to join a fitness group. Over the next two weeks, they were tested on how many push-ups they could do. The data shows the number of push-ups they did over the two weeks. From the first to the second week, what was the increase in the median number of push-ups?
Week 1: 5, 8, 10, 11, 6, 8, 9, 15, 5, 8
Week 2: 7, 9, 11, 12, 8, 10, 11, 18, 9, 10
(1 point)
First, we need to find the median of each week's data set.
For Week 1:
5, 8, 10, 11, 6, 8, 9, 15, 5, 8
The median is the middle number when the data is arranged in order:
5, 5, 6, 8, 8, 8, 9, 10, 11, 15
The median is 8.
For Week 2:
7, 9, 11, 12, 8, 10, 11, 18, 9, 10
The median is the middle number when the data is arranged in order:
7, 8, 9, 10, 11, 11, 12, 18
The median is 10.5.
To find the increase in median, we subtract the median for Week 1 from the median for Week 2:
10.5 - 8 = 2.5
So the increase in the median number of push-ups from the first to the second week is 2.5.
To find the increase in the median number of push-ups from the first to the second week, follow these steps:
Step 1: Sort the data for both weeks in ascending order:
Week 1: 5, 5, 6, 8, 8, 8, 9, 10, 11, 15
Week 2: 7, 8, 9, 10, 10, 11, 11, 12, 18, 2021
Step 2: Find the median for each week:
Week 1 median = (8 + 9) / 2 = 8.5
Week 2 median = (10 + 11) / 2 = 10.5
Step 3: Find the difference in medians:
Increase in median = Week 2 median - Week 1 median = 10.5 - 8.5 = 2
Therefore, the increase in the median number of push-ups from the first to the second week is 2.