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How would the median change if the number 71 replaced one of the 67's in the set?

71, 67, 67, 17, 69, 84, 21, 87

Question 5 options:

decrease


increase


no change

Sagot :

Hrishii

Answer:

increase

Step-by-step explanation:

  • Given data is: 71, 67, 67, 17, 69, 84, 21, 87

  • Arranging in ascending order we find: 17, 21, 67, 67, 69, 71, 84, 87

  • Here N = 8 (Even number)

  • N/2 = 4 and N/2 + 1 = 5

  • 4th term = 67, 5th term = 69

  • -> median = Sum of 4th and 5th term/2 = (67 + 69)/2 = 132/2 = 66

  • Now, when one of the 67 is replaced by 71, the new data set in ascending order will be: 17, 21, 67, 69, 71, 71, 84, 87

  • Here, 4th term = 69, 5th term = 71

  • New median = (69 + 71)/2 = 140/2 = 70

  • -> new median > initial median

CONCLUSION: Median will increase if the number 71 replaced one of the 67's in the set.

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