## Range and Mean

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### Range and Mean

by didieravoaka » Sat Apr 23, 2016 7:14 am

Thanks to help.

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by [email protected] » Sat Apr 23, 2016 10:01 am
Hi didieravoaka,

This question can be solved conceptually or by TESTing VALUES.

We're asked if the range of scores for one class equals the range of scores for a second class. This is a YES/NO question.

1) In each class, the number of students taking the quiz was 26, and the lowest score in each class was 70.

This tells us NOTHING about the ranges.

IF...
ALL the scores in the 1st class are 70 and ALL of the scores in the 2nd class are 70, then the answer to the question is YES.
ALL the scores in the 1st class are 70, but 25 of the scores in the 2nd class are 70 and 1 of the scores is a 71, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) In each class, the average (arithmetic mean) score on the quiz was 85

This tells us NOTHING about the ranges.

IF...
ALL the scores in the 1st class are 85 and ALL of the scores in the 2nd class are 85, then the answer to the question is YES.
ALL the scores in the 1st class are 85, but HALF of the scores in the 2nd class are 80 and HALF of the scores is a 90, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know...
In each class, the number of students taking the quiz was 26, and the lowest score in each class was 70.
In each class, the average (arithmetic mean) score on the quiz was 85

IF....
HALF the scores in the 1st class are 70 and HALF of the scores are 100 AND HALF of the scores in the 2nd class are 70 and HALF of the scores is a 100, then the answer to the question is YES.
HALF the scores in the 1st class are 70 and HALF of the scores are 100 AND 1/4 of the scores in the 2nd class are 70 and 3/4 of the scores are 90, then the answer to the question is NO.

Combined, INSUFFICIENT

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by OptimusPrep » Sun Apr 24, 2016 8:15 pm
didieravoaka wrote:

Thanks to help.
Required: Range of scores in Class 1 = Range of scores in class 2?

Statement 1: # of students in each class = 26. Lowest score in each class = 70
Range is the spread of values from the lowest to the highest.
From this statement, we just know the lowest value, but not the highest.
INSUFFICIENT

Statement 2: Average = 85
Average does not tells us anything about the range.
INSUFFICIENT

Combining both 1 and 2:
We have the average, the lowest and the # of students.
Still we cannot say anything about the highest marks.
INSUFFICIENT

Correct Option: E

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by ceilidh.erickson » Mon Apr 25, 2016 9:09 am
RANGE questions in DS are usually ones in which there is no formula to apply - you just have to test values and see if you can come up with different results. That can make these questions frustrating and time-consuming.

In my experience, DS questions about range are more likely to have a right answer of E than are other DS questions.
Ceilidh Erickson
EdM in Mind, Brain, and Education