To determine which value (mean, median, or mode) would change the most when adding the number 78 to the set, we can calculate each statistic before and after adding 78.
Original set: 57, 55, 21, 57, 50
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Mean:
- Original Mean = (57 + 55 + 21 + 57 + 50) / 5 = 240 / 5 = 48
- New Mean when adding 78 = (57 + 55 + 21 + 57 + 50 + 78) / 6 = (240 + 78) / 6 = 318 / 6 = 53
- Change in mean = 53 - 48 = 5
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Median:
- Original set sorted: 21, 50, 55, 57, 57
- Original Median = 55 (the middle number)
- New set with 78 included and sorted: 21, 50, 55, 57, 57, 78
- New Median = (55 + 57) / 2 = 56 (average of the two middle numbers)
- Change in median = 56 - 55 = 1
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Mode:
- Original mode = 57 (it appears most frequently, twice)
- The number 78 does not affect the frequency of existing numbers, so the mode remains 57.
- Change in mode = 57 - 57 = 0
Now, let's summarize the changes:
- Mean changed by 5
- Median changed by 1
- Mode changed by 0
Conclusion: The mean changes the most (by 5) when the number 78 is added to the set.