If the range of 23 grades is 20. The median is 80. How do find the highest and lowest score possible?

Question

How manay students scored 80 or above? and how many students scored 80 or below?

Answer 1

I disagree with the first two answerers...
The median is the data point dividing the higher half of a sample from the lower half. It is the data point where half the data points are equal or higher and half are equal or lower.

It is possible for the median to be equal to the highest value if half the values are equal to the highest value. Here is a sample set with the Range of 20 and the median of 80
{60, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80,...80}

Here is a different sample set with the same range and median but the max value is 100.
{80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, ...80, 100}

So the max value is 100 and the min value is 60, but they can't both occur in the same set.

Answer 2

The first two answers are incorrect because they are making the assumption that you have a normal distribution of scores around the mean (not median)

The median value is just the one value in the middle that separates the higher half of the values from the lower half of the values. The range is the difference between maximum and minimum values in a set.

So assuming we are talking about test scores with a maximum value of 100 the following can occur within a maximum range of 20 points.

The lowest possible score can be a 60.
The highest possible score can be a 100.
11 students will score 80 or below.
11 students will score 80 or above.
1 student will have to get an 80.

The highest possible and lowest possible values can not occur in the same set due to the max range of 20.

Answer 3

Median is a variation of "average", but you don't count how many are at any given value, so the highest and lowest are the only important ones.

Median = 80

Range = 20 (top = bottom+19)

50% of range = 10
High score will be 90, low will be 70.

Answer 4

if the range is 20 and the median is 80, then assuming the range is spread evenly around the median, the lowest score will be 70 and the highest will be 90