How many of the classes 27 students got more than 20 points?

Question

The class had a math test where max you could get was 40. The most successful student got 38 points. The classes mean was 21, and the classes median was 20. How many of the classes 27 students got more than 20 points?

Answer 1

There is a not enough information to really answer this problem.

 

If there are 27 pieces of data, the median is the middle score when the information is placed in increasing order.so 27/2 = 13.5.....which rounds to 14. This means that the 14th piece of data is the middle piece of data which is 20.

 

So the first 13 scores are 20 or below, the 14th score MUST be 20, since it's the value of the median, and the next 13 scores must all be 20 or higher. So there may be AT MOST, 13 scores higher than 20.....but there can be fewer. Here's an example of data that satisfies all of your conditions.

 

19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20,     20,      20, 22,22,22,22,22,22,22,22,22,22,22,38

first 13 pieces of data                                            median             next 13 pieces of data

 

Using this data, you'd have only 12 people higher than 20.

 

How about this example

 

19,19,19,19,19,19,19,19,19,19,19,19,19,           20,        20,20,20,20,20,20,20,20,20,20,31,31,38

This is the worst case scenario where the median is still 20, the mean is 21, you have 27 students, the highest is 38....but only 3 students got higher than 20.

 

Hope this helps....