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?

Question

Week 1: 5, 8, 10, 11, 6, 8, 9, 15, 5, 8
Week 2: 7, 9, 11, 12, 8, 10, 11, 18, 9, 10

Answer 1

To find the increase in the median number of push-ups from Week 1 to Week 2, we first need to calculate the median for each week.

Step 1: Organize the data for Week 1. The values for Week 1 are: 5, 8, 10, 11, 6, 8, 9, 15, 5, 8

First, we sort the data: 5, 5, 6, 8, 8, 8, 9, 10, 11, 15

Since there are 10 values (an even number), the median will be the average of the 5th and 6th values in the sorted list. The 5th value is 8 and the 6th value is also 8.

\[ \text{Median (Week 1)} = \frac{8 + 8}{2} = 8 \]

Step 2: Organize the data for Week 2. The values for Week 2 are: 7, 9, 11, 12, 8, 10, 11, 18, 9, 10

Now, we sort the data: 7, 8, 9, 9, 10, 10, 11, 11, 12, 18

Again, since there are 10 values, we take the average of the 5th and 6th values. The 5th value is 10 and the 6th value is also 10.

\[ \text{Median (Week 2)} = \frac{10 + 10}{2} = 10 \]

Step 3: Calculate the increase in the median. To find the increase in the median from Week 1 to Week 2: \[ \text{Increase} = \text{Median (Week 2)} - \text{Median (Week 1)} = 10 - 8 = 2 \]

Thus, the increase in the median number of push-ups from Week 1 to Week 2 is 2.