Question

The median for the following set of data, arranged in ascending order, is 5, and the range is 15. Calculate the mean of the data x, 3, y, 7, 16

Answer 1

Hi mate
here is your answer
median :- Value which occurred in the middle when arranged in ascending order
here ,median = 5= y

range = biggest value - smallest value
= 16-x= 15
X= 1

mean= sum of all observations/ no. of observations
(1+3+5+7+16)/5
6.4

hope it helps :)

Answer 2

Answer:

$\boxed{\bf{MEAN}\:=\:\mathsf{6.4}}$

Step-by-step explanation:

The data is already in ascending order :

Let n be the number of observations .

Here n is 5 .

When n is odd , $\bf{median}\: = \:\frac{n+1}{2}\sf{th\:observation}$

                                                    $\implies \frac{5+1}{2}\sf{th\:observation}$

                                                     $\implies \frac{6}{2}\sf{th\:observation}$

                                                     $\implies 3\bf{rd}\:\sf{th\:observation}$

The 3 rd observation from the given data is y.

The question says that the median is 5.

                                                         $\implies y\:=\:5$

The question also states that range of data is 15.

Range = upper limit - lower limit

           ==> 16 - x = 15

           ==> - x = 15 -16

           ==> - x = -1

           ==> x = 1

$\bf{Mean}\:=\:\mathsf{\frac{Sum\:of\:all\:observations}{5}}$

             $\implies \frac{x+3+y+7+16}{5}$

But as far as I remember y was found to be 5 and x was found to be 1

             $\implies \frac{1+3+5+7+16}{5}$

             $\implies \frac{9+23}{5}$

             $\implies \frac{32}{5}$

             $\implies 6.4$

The mean of the data is 6.4

Hope it helps you:-)

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