MEDIAN PRACTICE QUESTIONS

Question 1 :

A researcher studying the behavior of mice has recorded the time (in seconds) taken by each mouse to locate its food by considering 13 different mice as 31, 33, 63, 33, 28, 29, 33, 27, 27, 34, 35, 28, 32. Find the median time that mice spent in searching its food.

Solution :

 31, 33, 63, 33, 28, 29, 33, 27, 27, 34, 35, 28, 32

Ascending order of given data is

27, 27, 28, 28, 29, 31, 32, 33, 33, 33, 34, 35, 63

Middle value is 7^th observation

Median  =  32

Question 2 :

The following are the marks scored by the students in the Summative Assessment exam

N/2  =  50/2  =  25^th value

Median class =  20 - 30

l = 20, N//2  =  25, m = 9, f = 15 and c = 10

Median  =  20 + ([25 - 9]/15) x 10

  =  20 + (16/15) x 10

  =  20 + 1.06(10)

  =  20 + 10.6 

  =  30.6

Hence the median of the given data is 31.

Question 3 :

The mean of five positive integers is twice their median. If four of the integers are 3, 4, 6, 9 and median is 6, then find the fifth integer.

Solution :

Let "x" be the fifth observation.

Mean of 5 observations  =  (3 + 4 + 6 + 9 + x)/5

  =  (22 + x)/5

Median  =  6

Mean  =  2 median

(22 + x)/5  =  2(6)

22 + x  =  12(5)

22 + x  =  60

x  =  60 - 22

x  =  38

Hence the 5th observation is 38.

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