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
To find the median, we need to first put the numbers in order from least to greatest:
Week 1: 5, 5, 6, 8, 8, 9, 10, 11, 15
Week 2: 7, 8, 9, 10, 11, 11, 12, 18
The median of week 1 is 8, and the median of week 2 is 10. The increase in the median number of push-ups is 10 - 8 = 2 push-ups.
The range of the number of push-ups people did in Week 1 is 10.
The range of the number of push-ups people did in Week 2 is 11
The range of the number of push-ups people did in Week 1 is 10
To find the increase in the median number of push-ups from the first week 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
Step 2: Find the median for each week:
Week 1 median: The middle value is 8 because there are an even number of values, so we take the average of the two middle values (8 and 9).
Week 2 median: The middle value is also 10 because there are an odd number of values.
Step 3: Calculate the increase in the median:
The increase in the median number of push-ups is 10 - 8 = 2 push-ups.
Therefore, the increase in the median number of push-ups from the first week to the second week is 2 push-ups.