Median

A number or a quantity which represents the set of data is called central tendency.

The number of times a particular observation occurs in a given set of

data is called its frequency.


The total of a frequency and all frequencies below it in a frequency

distribution table is called cumulative frequency.



The difference between the upper limit and the lower limit of a class

interval is called its class size.


The median of a set of sorted data is the value of the observation which lies exactly half way along the set.

The class interval that contains the median is called median class.


To find the median of ungrouped data, first arrange all the terms in either ascending or descending order.

If there are odd number of terms, then median is

[(n+1)/2]th term

If there are even number of terms, then median is the average of

(n/2)th term and [(n/2) + 1]th term


For grouped data, median is calculated by the following formula:

Median = l + h × [(n/2) – cf]/f

Where,

l = lower limit of median class

n = number of observations

cf = cumulative frequency of class preceding the median class

f = frequency of median class

h = class size



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  • Q1

    Find the median class of the data.

    Class

    10-15

    15-20

    20-25

    25-30

    30-35

    frequency

    8

    6

    4

    7

    5

    Marks:1
    Answer:

    Class

    Frequency

    Cumulative Frequency

    10-15

    8

    8

    15-20

    6

    14

    20-25

    4

    18

    25-30

    7

    25

    30-35

    5

    30

    View Answer
  • Q2

    Find the median of the data.
    11, 12, 12, 10, 19, 17, 11

    Marks:1
    Answer:

    View Answer
  • Q3

    Find the median of the following set of numbers.
    10, 75, 3, 81, 18, 27, 4, 48, 12, 47, 9, 15

    Marks:1
    Answer:

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  • Q4

    A student secured the following marks in seven subjects – 50, 53, 61, 49, 45, 63, 48. Find the median score.

    Marks:1
    Answer:

    Arranging the marks in ascending order, we have
    45, 48, 49, 50, 53, 61, 63
    Since the series contain seven items, therefore, n = 7 and
    (n + 1)/2 = (7 + 1)/2
    = 8/2
    = 4

    Therefore, Md = size of 4th item = 50 marks

    View Answer
  • Q5

    Find the median of the data.
    10, 15, 12, 10, 19, 16, 11

    Marks:1
    Answer:

    View Answer