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Mode of 7 students scores is 87 , average is 80 , median 82, and lowes
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04 Jul 2025, 08:42
04 Jul 2025, 08:42
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Question Stats:
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Mode of 7 students scores is 87 , average is 80 , median 82, and lowest score is 70 . Calculate the maximum value of the highest score among 7 students, if scores are integer values?
Show: ::
91
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Re: Mode of 7 students scores is 87 , average is 80 , median 82, and lowes
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05 Jul 2025, 04:00
05 Jul 2025, 04:00
Expert Reply
Let 87 appear three times, and adjust other scores minimally:
- $S_1=70$,
- $S_2=70$,
- $S_3=70$,
- $S_4=82$,
- $S_5=87$,
- $S_6=87$,
- $S_7=94$.
- Sum: $\(70+70+70+82+87+87+94=560\)$.
$\({ }^{\circ}\)$ Mode: 70 appears three times, 87 appears twice. Invalid.
Step 6: Correct Strategy
To maximize $S_7$, while ensuring 87 is the strict mode:
1. Let 87 appear twice, and no other score appears more than once.
2. Set:
- $S_1=70$,
- $S_2=71$,
- $S_3=72$,
- $S_4=82$,
- $S_5=87$,
- $S_6=87$,
$\({ }^{\circ} S_7=560-(70+71+72+82+87+87)=560-469=91\)$.
3. Verify the mode:
- Scores: 70, 71, 72, 82, 87, 87, 91.
$\({ }^{\circ} 87\)$ appears twice; all others appear once. Valid.
Final Answer
The maximum possible highest score is:
91
- $S_1=70$,
- $S_2=70$,
- $S_3=70$,
- $S_4=82$,
- $S_5=87$,
- $S_6=87$,
- $S_7=94$.
- Sum: $\(70+70+70+82+87+87+94=560\)$.
$\({ }^{\circ}\)$ Mode: 70 appears three times, 87 appears twice. Invalid.
Step 6: Correct Strategy
To maximize $S_7$, while ensuring 87 is the strict mode:
1. Let 87 appear twice, and no other score appears more than once.
2. Set:
- $S_1=70$,
- $S_2=71$,
- $S_3=72$,
- $S_4=82$,
- $S_5=87$,
- $S_6=87$,
$\({ }^{\circ} S_7=560-(70+71+72+82+87+87)=560-469=91\)$.
3. Verify the mode:
- Scores: 70, 71, 72, 82, 87, 87, 91.
$\({ }^{\circ} 87\)$ appears twice; all others appear once. Valid.
Final Answer
The maximum possible highest score is:
91
gmatclubot
Re: Mode of 7 students scores is 87 , average is 80 , median 82, and lowes [#permalink]
05 Jul 2025, 04:00
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