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13 Jul 2025, 21:30
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Let me ask you this - why do you think every value should be 5 units away from mean? Think about how SD of a list is calculated. Think about what is meant when we say a value is 2SD away or 3SD away etc.
Komal324
03 Oct 2025, 20:35
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standard deviation is the AVERAGE DISTANCE FROM THE MEAN.
05 Jul 2026, 06:54
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Question:
The 10 students in a history class recently took an examination.
What was the maximum score?
Need an exact value.
---
Statement (1): Mean = 75
Total score = 10 × 75 = 750.
Can the maximum be different?
Case 1:
75, 75, 75, 75, 75, 75, 75, 75, 75, 75
Maximum = 75
Case 2:
50, 50, 50, 50, 50, 50, 50, 50, 50, 300
Maximum = 300
Different maxima.
Insufficient.
---
Statement (2): Standard deviation = 5
The standard deviation only tells us how spread out the scores are, not where they are centered.
Example:
70, 70, 70, 70, 70, 80, 80, 80, 80, 80
Mean = 75, SD = 5, Maximum = 80
Now add 10 to every score:
80, 80, 80, 80, 80, 90, 90, 90, 90, 90
Mean = 85, SD = 5, Maximum = 90
Adding a constant does not change standard deviation.
Different maxima.
Insufficient.
---
Together:
Mean = 75 and SD = 5.
Still not enough.
Example 1:
70, 70, 70, 70, 70, 80, 80, 80, 80, 80
Mean = 75.
Each score is 5 away from the mean, so variance = 25 and SD = 5.
Maximum = 80.
Example 2:
Let one score be 90 (+15 from mean) and another be 60 (-15). Their squared deviations contribute 225 each.
To keep total squared deviations = 10 × 25 = 250, the remaining eight students must have zero deviation:
75, 75, 75, 75, 75, 75, 75, 75, 60, 90
Mean = 75.
Sum of squared deviations = 225 + 225 = 450, so SD is not 5. This fails.
Need a valid second example.
Try:
65, 70, 75, 75, 75, 75, 75, 75, 80, 85
Mean = 75.
Squared deviations:
100 + 25 + 0 + ... + 25 + 100 = 250.
Variance = 250/10 = 25.
SD = 5.
Maximum = 85.
Thus we have:
Case 1: maximum = 80
Case 2: maximum = 85
Both satisfy the two statements.
So together they are still insufficient.
---
Answer: (E) Both statements together are not sufficient.
The 10 students in a history class recently took an examination.
What was the maximum score?
Need an exact value.
---
Statement (1): Mean = 75
Total score = 10 × 75 = 750.
Can the maximum be different?
Case 1:
75, 75, 75, 75, 75, 75, 75, 75, 75, 75
Maximum = 75
Case 2:
50, 50, 50, 50, 50, 50, 50, 50, 50, 300
Maximum = 300
Different maxima.
Insufficient.
---
Statement (2): Standard deviation = 5
The standard deviation only tells us how spread out the scores are, not where they are centered.
Example:
70, 70, 70, 70, 70, 80, 80, 80, 80, 80
Mean = 75, SD = 5, Maximum = 80
Now add 10 to every score:
80, 80, 80, 80, 80, 90, 90, 90, 90, 90
Mean = 85, SD = 5, Maximum = 90
Adding a constant does not change standard deviation.
Different maxima.
Insufficient.
---
Together:
Mean = 75 and SD = 5.
Still not enough.
Example 1:
70, 70, 70, 70, 70, 80, 80, 80, 80, 80
Mean = 75.
Each score is 5 away from the mean, so variance = 25 and SD = 5.
Maximum = 80.
Example 2:
Let one score be 90 (+15 from mean) and another be 60 (-15). Their squared deviations contribute 225 each.
To keep total squared deviations = 10 × 25 = 250, the remaining eight students must have zero deviation:
75, 75, 75, 75, 75, 75, 75, 75, 60, 90
Mean = 75.
Sum of squared deviations = 225 + 225 = 450, so SD is not 5. This fails.
Need a valid second example.
Try:
65, 70, 75, 75, 75, 75, 75, 75, 80, 85
Mean = 75.
Squared deviations:
100 + 25 + 0 + ... + 25 + 100 = 250.
Variance = 250/10 = 25.
SD = 5.
Maximum = 85.
Thus we have:
Case 1: maximum = 80
Case 2: maximum = 85
Both satisfy the two statements.
So together they are still insufficient.
---
Answer: (E) Both statements together are not sufficient.
