Marks in statistics of 12 students are x, 28, 35, 56, 78, 63, 65, 81, 79, 83, 80, y, where x and y are the lowest and highest marks, respectively. If the range and average of the marks are 70 and 64, respectively, then the ordered pair (x, y) is:
Given:
Marks: (x, 28, 35, 56, 78, 63, 65, 81, 79, 83, 80, y)
x = lowest, y = highest
Range = 70
y - x = 70
Average = 64
Formula Used:
Sum =
Range = Max - Min
Solution:
total of 12 marks = 6
Sum of known 10 marks
28 + 35 + 56 + 78 + 63 + 65 + 81 + 79 + 83 + 80 = 648.
So,
x + y + 648 = 768
x + y = 120
Also,
y - x = 70
Solve the system:
Now,
2y = 190
y = 95
x = 120 - 95 = 25.
(x, y) = (25, 95)
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