If crystal scored 81, 90, and 95 on her science exams, what score would she need on her next exam in order for her mean and her median scores to be the same

Question

Please show work&how to do it Thank you!

Answer 1

If crystal scored 81, 90, and 95 on her science exams, what score would she need on her next exam in order for her mean and her median scores to be the same

mean is the average

median is the middlest

So for the average to equal the middles, lets look at the formula for each:

Average = (81 + 90 + 95 + X)/4

Median = (X + 90)/2 * I used 90 and the latest test score because 81 and 95 are outliers.

now set these two expression equal such as:

Average = Median

(81 + 90 + 95 + X)/4 = (X + 90)/2 * Solve for X

(266 + X)/4 = (90 + X)/2 * Cross Multiply

2(266 + X) = 4(90 +X)

532 + 2X = 360 + 4X

2X = 172

X = 86

Answer, the student needs 86 points to make the mean and the median equal.