mean question of statistics.

Question

the mass of a group of children are 9,11,13,13,15,15,15,a,18,20. given that the median mass is 0.4 greater than the mean mass, find the value of a and state the modal mass.

Answer 1

9,11,13,13,15,15,15,a,18,20

 

Since there are an even number of data points, look at the two in the middle

and average those two terms to find the median.  The 5th and 6th terms are

both 15 so the median is 15.

 

median mass is 0.4 greater than the mean:

15 = mean + 0.4

mean = 15 - 0.4

mean = 14.6

 

(9+11+13+13+15+15+15+a+18+20)/10 = 14.6

 

9+11+13+13+15+15+15+a+18+20 = 146

129 + a = 146

a = 17

 

The mode is 15 since it appears more often than any other data point