Bot, 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 increase in the median number of push-ups, we need to first find the median of each week's data set.
Week 1 median: (5, 5, 6, 8, 8, 9, 10, 11, 15) = 8
Week 2 median: (7, 8, 9, 10, 11, 11, 12, 18) = 10
The increase in the median number of push-ups is 10 - 8 = 2. So the median number of push-ups increased by 2 from the first week to the second week.
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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
Step 2: Calculate the median for each week. The median is the middle number in the sorted list. If there is an odd number of values, take the middle one. If there is an even number of values, take the average of the two middle numbers.
Week 1 median: 8
Week 2 median: 10
Step 3: Calculate the difference between the two medians.
Week 2 median - Week 1 median = 10 - 8 = 2
Therefore, the increase in the median number of push-ups from the first to the second week is 2.