Question

If the mean of 7 observations 28,X,32,43,X+3,X+5 and 45 is 38, find X. Hence find median​

Answer 1

Mean of 7 observations 28, x, 32, 43, x+2, x+5 and 45 is 38. So, the value of x is 37. ... Median = (N+1)/2 ; where 'N' is number of observations.

Answer 2

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.