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:

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RRB NTPC Graduate Level CBT-I Official Paper (Held On: 05 Jun, 2025 Shift 2)

Answer 1

Given:

Marks of 12 students: x, 28, 35, 56, 78, 63, 65, 81, 79, 83, 80, y

Range = 70

Average = 64

x = Lowest mark, y = Highest mark

Formula used:

Range = y - x

Average = \(\dfrac{\text{Sum of all marks}}{\text{Total number of students}}\)

Calculation:

Range = y - x

⇒ 70 = y - x

⇒ y = x + 70

Average = \(\dfrac{\text{Sum of all marks}}{12}\)

⇒ 64 = \(\dfrac{x + 28 + 35 + 56 + 78 + 63 + 65 + 81 + 79 + 83 + 80 + y}{12}\)

⇒ 64 × 12 = x + 28 + 35 + 56 + 78 + 63 + 65 + 81 + 79 + 83 + 80 + y

⇒ 768 = x + y + (28 + 35 + 56 + 78 + 63 + 65 + 81 + 79 + 83 + 80)

⇒ 768 = x + y + 648

⇒ x + y = 768 - 648

⇒ x + y = 120

Solving for x and y:

From y = x + 70 and x + y = 120, substitute y = x + 70:

⇒ x + (x + 70) = 120

⇒ 2x + 70 = 120

⇒ 2x = 120 - 70

⇒ 2x = 50

⇒ x = 25

Substitute x = 25 in y = x + 70:

⇒ y = 25 + 70

⇒ y = 95

∴ The ordered pair (x, y) = (25, 95).

The correct answer is option (3).

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