Question

if the mean of 7 observations 28,x,32,43,x+2,x+5 and 45 is 38 find x hence.find median.

Answer 1

Solution:-
Given : Mean of 7 observations 28, x, 32, 43, x+2, x+5 and 45 is 38.
So,
Mean = Sum of all observations/Number of observations
38 = (28 + x + 32 + 43 + x+2 + x+5 + 45)/7
38 = (3x + 155)/7
3x + 155 = 38*7
3x = 266 - 155
3x = 111
x = 111/3
x = 37
So, the value of x is 37.
The missing values in these are 37, (37 + 2) = 39 and (37 + 5) = 42
Now, the observations are 28, 37, 32, 43, 39, 42 and 45

Now, 
For calculation of median, we have to arrange this in ascending order.
Ascending order = 28, 32, 37, 39, 42, 43, 45
Median = (N+1)/2  ; where 'N' is number of observations.
= (7+1)/2
= 8/2
= 4
4th item is 39. 
So, The Median is 39
Answer. 

Answer 2

Mean of 7 observations
=(28+x+32+43+x+2+x+5+45)/7=38
or, (3x+155)/7=38
or, 3x+155=38×7
or, 3x=266-155
or, x=111/3
or, x=37
∴, x+2=39 and x+5=42
Now, there are 7 observations, 28,32,37,39,42,43,45 (in ascending order)
∴, Median=(n+1)/2 th value where n=7
or, Median=(7+1)/2 th value
or, Median=8/2 th value
or, Median=4th value =39
∴, x=37 and Median=39 Ans.