On a certain math exam, 10% of the students got 70 points, 25% got 80

We can let the number of students = 100, thus:

10 had a 70

25 had an 80

20 had an 85

15 had a 90

30 had a 95

The median position is (100 + 1)/2 = 50.5, i.e., the average of the 50th and 51st numbers. We see that they both are 85, so the median is also 85.

The mean is:

(10 x 70 + 25 x 80 + 20 x 85 + 15 x 90 + 30 x 95)/100

(700 + 2000 + 1700 + 1350 + 2850)/100

8600/100

86

So the difference between the mean and the median is 86 - 85 = 1.

Answer: B

First, imagine we have 100 students taking this exam. This makes the percentages easy to work with:

• 10 students scored 70 points.
• 25 students scored 80 points.
• 20 students scored 85 points.
• 15 students scored 90 points.
• The remaining students got 95 points. To find "the rest," we add up the percentages we know: 10%+25%+20%+15%=70%. So, 100%−70%=30% of students got 95 points. This means 30 students scored 95 points.

Now, let's calculate the Mean Score (Average):
To find the average, we sum up all the scores and divide by the total number of students.

• (10 students×70 points)=700
• (25 students×80 points)=2000
• (20 students×85 points)=1700
• (15 students×90 points)=1350
• (30 students×95 points)=2850

Total points: 700+2000+1700+1350+2850=8600 points. Total students: 10+25+20+15+30=100 students.
Mean Score =Total StudentsTotal Points=1008600=86 points.
Next, let's find the Median Score (Middle Value):
To find the median, we need to line up all 100 scores in order from lowest to highest and find the value in the middle. Since we have an even number of students (100), the median will be the average of the 50th and 51st scores.
Let's imagine listing out the scores:

• The first 10 scores are 70.
• The next 25 scores are 80. So, scores from position 11 to 35 are 80.
• The next 20 scores are 85. So, scores from position 36 to 55 are 85.
  
  • This is important! Both the 50th student and the 51st student fall within this group who scored 85.
• The next 15 scores are 90. So, scores from position 56 to 70 are 90.
• The last 30 scores are 95. So, scores from position 71 to 100 are 95.

Since both the 50th and 51st scores are 85, the Median Score =285+85=85 points.
Finally, the Difference:
Difference = Mean Score - Median Score Difference = 86−85=1
So, the mean score is 86, the median score is 85, and their difference is
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First, imagine we have 100 students taking this exam. This makes the percentages easy to work with:

10 students scored 70 points.

25 students scored 80 points.

20 students scored 85 points.

15 students scored 90 points.

The remaining students got 95 points. To find "the rest," we add up the percentages we know: 10%+25%+20%+15%=70%. So, 100%−70%=30% of students got 95 points. This means 30 students scored 95 points.

Now, let's calculate the Mean Score (Average):

To find the average, we sum up all the scores and divide by the total number of students.

(10 students×70 points)=700

(25 students×80 points)=2000

(20 students×85 points)=1700

(15 students×90 points)=1350

(30 students×95 points)=2850

Total points: 700+2000+1700+1350+2850=8600 points.
Total students: 10+25+20+15+30=100 students.

Mean Score =
Total Students
Total Points

=
100
8600

=86 points.

Next, let's find the Median Score (Middle Value):

To find the median, we need to line up all 100 scores in order from lowest to highest and find the value in the middle. Since we have an even number of students (100), the median will be the average of the 50th and 51st scores.

Let's imagine listing out the scores:

The first 10 scores are 70.

The next 25 scores are 80. So, scores from position 11 to 35 are 80.

The next 20 scores are 85. So, scores from position 36 to 55 are 85.

This is important! Both the 50th student and the 51st student fall within this group who scored 85.

The next 15 scores are 90. So, scores from position 56 to 70 are 90.

The last 30 scores are 95. So, scores from position 71 to 100 are 95.

Since both the 50th and 51st scores are 85, the Median Score =
2
85+85

=85 points.

Finally, the Difference:

Difference = Mean Score - Median Score
Difference = 86−85=1

So, the mean score is 86, the median score is 85, and their difference is

Free GMAT diagnostic test from Career Launcher:
https://2ly.link/2Alsw