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Q24.
Yusuf sat 8 examinations. Here are his marks for 5 of the examinations: 68, 72, 75, 77, 80.
For his results in all 8 examinations, the mode of his marks is 80, the median of his marks is 74, and the range of his marks is 16.
Find Yusuf's marks for each of the other 3 examinations.

Q25.
30 students in a class sat a Mathematics test. The mean mark in the test for the 30 students was 26.8. 13 of the 30 students in the class are boys, and the mean mark in the test for the boys was 25.
Find the mean mark in the test for the girls. Give your answer correct to 3 significant figures.

Answer :

To solve these questions, we'll approach them step-by-step.

Q24:
Yusuf sat 8 examinations, with some given information:

  • Known marks: 68, 72, 75, 77, 80
  • Mode of all marks: 80
  • Median of all marks: 74
  • Range of all marks: 16

  1. Mode: Since the mode of his marks is 80, it must appear more than once among all 8 marks.

  2. Range: The range is the difference between the highest and lowest marks. Since we're given the range is 16, and 80 is one of the marks, the lowest mark is 80 - 16 = 64.

  3. Median: The median of 8 numbers is the average of the 4th and 5th marks when arranged in order. The median is 74.

Given marks: 64, 68, 72, 75, 77, 80, and at least one more 80 to satisfy the mode condition. Let's try to complete the sequence: [64, 68, 72, 75, X, Y, 77, 80], aiming for the median at the 4th and 5th positions.

If we assume X = 74 (considering the median), then:

  • 64, 68, 72, 74, 75, 77, 80,

We still need one more 80 to be the mode:

  • 64, 68, 72, 74, 75, 77, 80, 80

Therefore, Yusuf's marks for the other 3 examinations are 64, 74, and another 80.

Q25:
We know:

  • Total students: 30
  • Mean mark for all students: 26.8
  • Boys: 13
  • Mean mark for boys: 25

To find the mean for the girls, we first need the total marks:

  1. **Total Marks for All Students: 30 ffffffffffffffffffffffffffffffffffffffffffff=
    ]
    = \ 804
    ]

Totaline marks for Bayes :100 113&5[tex]= 13 1 25 =
der approxima total mark for girls:ly[/tex]
[tex]\ = 804–325=479[/tex]

Since are total girls =
der approxima girls' mean mark:

[tex]\ 2 \ = 16 1 \ &= 2023 \ 1 = 29.9375[/tex]

Rounded to 3 significant figures, the mean mark for the girls is 29.9.

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