Question

A student's average (arithmetic mean) test score on $4$ tests is $78$.What must be the student's score on a $5^{th}$ test for the student's average score on the $5$ tests to be $80$?

• A. $80$
• B. $82$
• C. $84$
• D. $86$
• E. $88$

Answer 1

Answer: (E)

$88$

Mean (average) is the sum of the data values divided by the total number of values in the data set.

Given that average of $4$ tests score is $98$

Let the $4$ tests scores be $a_1,a_2,a_3,a_4$

$⟹\frac{a_1+a_2+a_3+a_4}{4}=78$

$⟹a_1+a_2+a_3+a_4=312$ -------(1)

Let the $5^{th}$ test score be $x_5$

Given that average score of $5$ tests is $80$

$⟹\frac{a_1+a_2+a_3+a_4+a_5}{5}=80$

$⟹a_1+a_2+a_3+a_4+a_5=400$ -------(2)

Substituting (1) in (2) we get

$312+a_5=400$

$⟹a_5=400-312=88$