Question

Enter a number. Five students submitted their tests and it turned out that the mean of their grades was also the median: 78. The lowest grade was 62, and the range of their grades was 32. Two students submitted their tests late; however, their grades did not affect the mean and median grade. One grade turned out to be 56. The seventh student's grade was

Answer 1

*** FIRST CASE***

numer of students (n) = 5

mean () = 78

T

hence, we have,

$\frac{1}{n}\sum_{i=1}^{5} x_{i}=78$

$\Rightarrow \frac{1}{5}\sum_{i=1}^{5} x_{i}=78$

$\Rightarrow \sum_{i=1}^{5} x_{i}=78*5 = 390$

*** SECOND CASE***

number of students (n) = 7

mean remains the same as in the first case.

let, the seventh student's grade be a.

according to the problem:-

$\bar{x}=78$

$\Rightarrow \frac{1}{7}(\sum_{i=1}^{5} x_{i}+56+a)=78$

$\Rightarrow 390+56+a=78*7= 546$

$\Rightarrow a=546-(390+56)$

$\Rightarrow\mathbf{ a=100}$

the seventh student's grade was = 100

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