FINDING MEDIAN FOR UNGROUPED DATA

Problem 1 :

2, 5, 1, 5, 2, 1, 2, 3, 2, 3, 1

Solution :

Ascending order of the given data

1, 1, 1, 2, 2, 2, 2, 3, 3, 5, 5

Number of values given = 11 (odd)

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

Median = 12/2 = 6^th value

Hence the median is 2.

Problem 2 :

8, 5, 1, 3, 7, 1, 1, 7, 1, 8, 7

Solution :

Ascending order of the given data

1, 1, 1, 1, 3, 5, 7, 7, 7, 8, 8

Number of values given = 11 (odd)

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

Median = 12/2 = 6^th value

Hence the median is 5.

Problem 3 :

18, 22, 17, 20, 19, 20, 22, 19, 29, 18, 23, 25, 22, 24, 23, 22, 18, 20, 22, 20

Solution :

Ascending order of the given data 

17, 18, 18, 18, 19, 19, 20, 20, 20, 20, 22, 22, 22, 22, 22, 23, 23, 24, 25, 29

Number of given observations = 20

Median = [(N/2)^th observation + ((N/2) + 1)^th observation] / 2

Median = [(20/2)^th value + ((20/2) + 1)^th value] / 2

= (10^th value + 11^th value) / 2

= (20 + 22) / 2

= 42/2

= 21

Problem 4 :

42, 28, 32, 35, 24, 32, 48, 32, 32, 24, 35, 28, 30, 35, 45, 32, 28, 32, 42, 42, 30

Solution :

Ascending order of the given data

24, 24, 28, 28, 28, 30, 30, 32, 32, 32, 32, 32, 32, 35, 35, 35, 42, 42, 42, 45, 48

Number of values given = 21 (odd)

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

Median = 22/2 = 11^th value

Hence the median is 32.

Problem 5 :

The number of children per house on one block:

1, 4, 2, 3, 3, 2, 6, 2, 4, 2, 0, 3, 0.

Solution :

Ascending order of the given data

0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 6

Number of values given = 13 (odd)

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

Median = 14/2 = 7^th value

Hence the median is 2.

Problem 6 :

The number of movies watched each month last year: 2, 0, 3, 0, 0, 8, 6, 5, 0, 1, 2, 3

Solution :

Ascending order of the given data

0, 0, 0, 0, 1, 2, 2, 3, 3, 5, 6, 8

Number of given observations = 12

Median = [(N/2)^th observation + ((N/2) + 1)^th observation] / 2

Median = [(12/2)^th value + ((12/2) + 1)^th value] / 2

= (6^th value + 7^th value) / 2

= (2 + 2) / 2

= 4/2

= 2

Problem 7 :

The number of units being taken by students in one class: 12, 5, 11, 10, 10, 11, 5, 11, 11, 11, 10, 12.

Solution :

Ascending order of the given data

5, 5, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12

Number of given observations = 12

Median = [(N/2)^th observation + ((N/2) + 1)^th observation] / 2

Median = [(12/2)^th value + ((12/2) + 1)^th value] / 2

= (6^th value + 7^th value) / 2

= (11 + 11) / 2

= 22/2

= 11

Problem 8 :

The number of hours of sleep per night for the past two weeks: 8, 5, 7, 8, 8, 6, 6, 6, 6, 9, 7, 8, 8, 8.

Solution :

Ascending order of the given data

5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9

Number of given observations = 12

Median = [(N/2)^th observation + ((N/2) + 1)^th observation] / 2

Median = [(14/2)^th value + ((14/2) + 1)^th value] / 2

= (7^th value + 8^th value) / 2

= (7 + 8) / 2

= 15/2

= 7.5