Lauren's scores on her math tests were 96, 95, 99, 91, 94, 93, and 97. What score could Lauren get on her next math test so that the mean and median remain the same? Complete the explanation.

Answer 1

91 93 94 95 96 97 99 upon sorting

The mean of these statistics is in fact 95.

The MEDIAN of these statistics is also 95.

The TOTAL of these statistics is 665.

So it stands to reason that by adding 95 to the data set,

the mean and median will both still be 95.

Here is the algebraic solution., Read on if you are interested......................

Upon adding statistic X to the data set, the NEW median shall be

(X + 95)/ 2

because then there will be 8 statistics, which requires the average

of the two middle ones to find the median.

The NEW mean shall be (665+x)/8

Therefore, (665 + X)/8 = (X+95)/2

665 + x = (x+95)*4 <--- multiplies both sides by 8

x + 665 = 4x + 380

665 = 4x + 380 - x

665 = 3x + 380

285 = 3x

x = 95