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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

The range of the number of push-ups did in Week 1 is __.
The range of the number of push-ups did in Week 2 is __.

1 answer

To find the increase in the median number of push-ups from Week 1 to Week 2, as well as the ranges for both weeks, let's follow these steps:

  1. Calculate the median for Week 1.

    • Week 1 data: 5, 8, 10, 11, 6, 8, 9, 15, 5, 8
    • First, sort the data: 5, 5, 6, 8, 8, 8, 9, 10, 11, 15
    • Since there are 10 data points (an even number), the median is the average of the 5th and 6th values:
      • 5th value = 8
      • 6th value = 8
    • Median for Week 1 = (8 + 8) / 2 = 8

  2. Calculate the median for Week 2.

    • Week 2 data: 7, 9, 11, 12, 8, 10, 11, 18, 9, 10
    • First, sort the data: 7, 8, 9, 9, 10, 10, 11, 11, 12, 18
    • Again, for the 10 data points, the median is the average of the 5th and 6th values:
      • 5th value = 10
      • 6th value = 10
    • Median for Week 2 = (10 + 10) / 2 = 10

  3. Calculate the increase in the median from Week 1 to Week 2.

    • Increase = Median Week 2 - Median Week 1 = 10 - 8 = 2

  4. Calculate the range for Week 1.

    • Range = Maximum value - Minimum value
    • Maximum value in Week 1 = 15
    • Minimum value in Week 1 = 5
    • Range for Week 1 = 15 - 5 = 10

  5. Calculate the range for Week 2.

    • Maximum value in Week 2 = 18
    • Minimum value in Week 2 = 7
    • Range for Week 2 = 18 - 7 = 11

Summary of results:

  • The increase in the median number of push-ups from Week 1 to Week 2 is 2.
  • The range of the number of push-ups done in Week 1 is 10.
  • The range of the number of push-ups done in Week 2 is 11.