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
1015
1520
2025
2530
3035
frequency
8
6
4
7
5
Marks:1Answer:
Class
Frequency
Cumulative Frequency
1015
8
8
1520
6
14
2025
4
18
2530
7
25
3035
5
30

Q2
Find the median of the data.
11, 12, 12, 10, 19, 17, 11Marks:1Answer:

Q3
Find the median of the following set of numbers.
10, 75, 3, 81, 18, 27, 4, 48, 12, 47, 9, 15Marks:1Answer:

Q4
A student secured the following marks in seven subjects – 50, 53, 61, 49, 45, 63, 48. Find the median score.
Marks:1Answer:
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, M_{d} = size of 4^{th} item = 50 marks 
Q5
Find the median of the data.
10, 15, 12, 10, 19, 16, 11Marks:1Answer: