20 Students each have either 0,1,2 and 3 cars. The median is 1.5 cars and the mean is 1.4 cars per student. How many students (if 4 have 0 cars) have 0,1,2 and

Question

20 Students each have either 0,1,2 and 3 cars. The median is 1.5 cars and the mean is 1.4 cars per student. How many students (if 4 have 0 cars) have 0,1,2 and 3 cars?

I know how to find the median, but figuring out which things to add and then divide by what to get the mean has stumped me even though it seems simple 

Answer 1

You have 20 students in total and 4 have 0 cars, so 16 students have 1,2 or 3 cars.

 

Since there are 20 students, an even number, there is not one single middle score, so the median is found by taking the average of the 10th and 11th piece of data. Since the average is 1.5, the 10th piece of data must be a 1 and the 11th piece of data must be a 2 so that they average to a median of 1.5.

 

So the first 4 numbers are 0,0,0,0, and the next six must be 1,1,1,1,1,1 and the 11th piece of data is a 2. That leaves us with 9 more spots to fill......with 2s and 3s.

 

The mean is 1.4. The mean = Sum of data/number of data.....1.4=sum/20.....so the sum is 20*1.4=28.

The data that you already have adds up to 8, so the remaining 9 pieces of data must sum to 20....and it's made up of only 2s and 3s. Well 9 2's would add to 8...so I need 7 more 2's and 2 3's...which is 14+6=20.

 

So my original data must be 0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3.

That's 4 0's, 6 1's, 8 2's and 2 3's.

 

Hope this helped.