Median is the value which occupies the middle position when all the observations are arranged in an ascending or descending order. It is a positional average.
(i) Arrange the data in ascending ( or) decending order of magnitude.
(ii) Construct the cumulative frequency distribution. Let N be the total frequency
(iii) If N is odd, median = [(N + 1)/2]^{th} observation.
(iv) If N is even, median
= [(N/2)^{th} observation + ((N/2) + 1)^{th} observation]/2
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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