FINDING MEDIAN FOR UNGROUPED DATA

Question 1 :

Find the median of the given values : 47, 53, 62, 71, 83, 21, 43, 47, 41.

Solution :

Ascending order of the given data 

21, 41, 43, 47, 47, 53, 62, 71, 83

Number of values given  =  9 (odd)

  median  =  [(N + 1)/2]^th value

  Median  =  10/2  =  5th value.

Hence the median is 47.

Question 2 :

Find the Median of the given data: 36, 44, 86, 31, 37, 44, 86, 35, 60, 51

Solution :

Ascending order of the given data.

31, 35, 36, 37, 44, 44, 51, 60, 86, 86

Number of given observations  =  10

Median  =  (10/2) th value + [(10/2) + 1] th value

=  (5th value + 6th value)/2

=  (44 + 44)/2

=  44

Question 3 :

The median of observation 11, 12, 14, 18, x + 2, x + 4, 30, 32, 35, 41 arranged in ascending order is 24. Find the values of x.

Solution :

The given data is in ascending order.

Number of observations of the given data is 10

Median is average of 5^th and 6^th observation.

[(x + 2) + (x + 4)]/2  =  24

2x + 6  =  48

2x  =  48 - 6

2x  =  42

x  =  21

Hence the value of x is 21.

Question 4:

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

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