10 students participated in a quiz. What was the standard deviation of

Question

10 students participated in a quiz. What was the standard deviation of their scores?
 
(1) The median of the students’ scores was equal to the highest score in the group.
(2) The median of the students’ scores was equal to the lowest score in the group.

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Adit_ · Answer

Statement 1 has no info on the left side of distribution at all, it HOWEVER does say that all values on right side are equal. Keep this
NOT SUFFICIENT

Statement 2 is similar tell us that left side are all equal 
NOT SUFFICIENT

Combining both:

Left side=Median
Right=Median
Left Side element = Right side elements

SD=0 (All elements are equal thus no deviation from Mean)

Answer:  C

Dereno · Answer

There are ten students, so the median values are between value 5 and 6.

And we are asked to find the standard deviation, which is related to the mean.

Mean depends on the individual values.

Statement 1:

The median of the students’ scores was equal to the highest score in the group.

so, the values from 5th to 10th remains the same equal to the highest score. Say 80.

The remaining 4 values can be either as low as 0, or to the max 80.

Mean can vary between 48 and 79.6 or 80.

Hence, the standard deviation cannot be calculated precisely. Hence,  Insufficient

Statement 2:

The median of the students’ scores was equal to the lowest score in the group.

So, the values from 1 to 6, occupies the same value say 10.

and from 7 to 10, can be either 10, or any other positive integer greater than 10.

so, the mean can vary depending on the extreme values. So, is the standard deviation.

Hence,  Insufficient

Combining both statements we get

All the values remain the same.

so, the values from lowest to the highest is same as the median = Mean.

Thus, the  standard deviation =0.

Option C

Navdeep2000 · Answer

As we know, SD in its basic terms is the distance of the terms from the mean of its set.

(1) The median of the students’ scores was equal to the highest score in the group.
 This tells us that 5th - 10th term here are all equal. However, the same cannot be said with certainty for the first 4 terms. 
 They may or may not all be identical.  Not sufficient

(2) The median of the students’ scores was equal to the lowest score in the group. 
 This tells us that 1st-6th term in the set are all identical. However, the same cannot be said with certainty for the last 4 terms.  
 Again, they may or may not all be identical.  Not sufficient

(1)+(2) When we combine both the options together, we can surely say that all the terms in the set are identical to each other. And by the property of SD, when all the terms are equal to each other, SD=0 since there is no distance between any term with that the mean of the set. Thus, Sufficient together.  Option C

egmat · Answer

Standard deviation = 0 when ALL values are identical.  So the real question becomes: Can we determine if all 10 scores are the same?

Understanding the Median: 
With  10  students, the median is the average of the  5th  and  6th  scores when arranged in order.

Statement 1:  Median = Highest score
If the average of the 5th and 6th scores equals the highest score, then positions 5, 6, and all scores above must equal the highest (you can't average two numbers and get something higher than both).

But what about positions 1-4?  They could be lower!

Case 1:  All scores =  80  → Median = 80 = Highest ✓ → SD =  0 
 Case 2:  Scores: {70, 70, 70, 70, 80, 80, 80, 80, 80, 80} → Median = 80 = Highest ✓ → SD ≠  0

Two different SD values possible.  Not Sufficient.

Statement 2:  Median = Lowest score
By similar logic, positions 1 through 6 must all equal the lowest score.

But what about positions 7-10?  They could be higher!

Case 1:  All scores =  80  → Median = 80 = Lowest ✓ → SD =  0 
 Case 2:  Scores: {70, 70, 70, 70, 70, 70, 80, 80, 80, 80} → Median = 70 = Lowest ✓ → SD ≠  0

Two different SD values possible.  Not Sufficient.

Both Statements Together: 
 Median = Highest AND Median = Lowest 
→ Highest score = Lowest score
→ ALL scores must be identical!
→ SD =  0  (always)

Answer: C

ExpertsGlobal5 · Answer

Explanation Video:

https://www.youtube.com/watch?v=zM1SFNVPKTY

10 students participated in a quiz. What was the standard deviation of

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GMAT Data Sufficiency (DS) Questions

10 students participated in a quiz. What was the standard deviation of

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