2. Find x and y so that the ordered data set has a mean of 42 and a median of 35. 17 , 22 , 26 , 29 , 34 , x , 42 , 67 , 70 , y

Question

2. Find x and y so that the ordered data set has a mean of 42 and a median of 35.

17 , 22 , 26 , 29 , 34 , x , 42 , 67 , 70 , y

 

Answer 1

Because the median is the average of the 5th & 6th items of data (because n = 10), the 6th item, x, must be 36 so that the median comes out to be 35.

 

Then the sum of the first 9 items is 307 + 36 =343; the sum of all ten items is 343 + y

and mean = (343 + y) /10 = 42.  This gives y = 420 - 343 = 77

Answer 2

If the median is 35 that tells you the average of 34 and x.

 

This allows you to calculate x.

 

Once you have x you know that the sum of all the numbers divided by 10 must be 42 and this will let you find y.