The mean mark of a student in 6 tests is 14. When the highest and lowest marks, which diff… — JAMB UTME

The mean mark of a student in $6$ tests is $14$ . When the highest and lowest marks, which differ by $12$ , are excluded, the mean mark of the remaining $4$ tests becomes $13.5$ . What is the highest mark?

Answer: 21

Answer

The highest mark is 21.

The total sum of all 6 tests is

6 \times 14 = 84

. When the highest (

H

) and lowest (

L

) marks are removed, the total sum of the remaining 4 tests is

4 \times 13.5 = 54

. The sum of the excluded marks is

H + L = 84 - 54 = 30

. Knowing that their difference is

H - L = 12

, we add the two equations to get

2H = 42

, which gives

H = 21

Step-by-Step Solution

Calculate the total sum of all 6 test marks

Sum of 6 marks =

6 \times 14 = 84

The sum of data values equals the mean multiplied by the number of items.

Calculate the sum of the remaining 4 test marks

Sum of 4 marks =

4 \times 13.5 = 54

Multiplying the new mean by 4 gives the sum of the test scores excluding the highest and lowest values.

Determine the combined sum of the highest (H) and lowest (L) marks

H + L = 84 - 54 = 30

Subtracting the sum of the 4 remaining marks from the total initial sum yields the sum of the two excluded marks.

Solve for H using the simultaneous linear equations

H = 21

Adding H + L = 30 and H - L = 12 gives 2H = 42, which solves to H = 21.

Key Concept

Mean of Ungrouped Data and Handling Excluded Values

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