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 of push-ups? Week 1: 1,5,8,10,11,6,8,9,15,5,8. Week 2: 2,7,9,11,12,8,10,11,18,9,10.
To find the increase in the median of push-ups from the first week to the second week, first, we need to find the medians of both data sets.
For the first week:
1, 5, 8, 10, 11, 6, 8, 9, 15, 5, 8
The median is the middle number when the data is arranged in numerical order. Since there are 11 numbers, the median will be the average of the 6th and 7th numbers.
Arranging the data in numerical order:
1, 5, 5, 6, 8, 8, 8, 9, 10, 11, 15
The median is (8 + 8) / 2 = 8
For the second week:
2, 7, 9, 11, 12, 8, 10, 11, 18, 9, 10
The median is the middle number when the data is arranged in numerical order. Since there are 11 numbers, the median will be the 6th number.
Arranging the data in numerical order:
2, 7, 8, 9, 9, 10, 10, 11, 11, 12, 18
The median is 10
Therefore, the increase in the median of push-ups from the first week to the second week is 10 - 8 = 2.