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 ofdata is called its frequency.The total of a frequency and all frequencies below it in a frequencydistribution table is called cumulative frequency.The difference between the upper limit and the lower limit of a classinterval 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 termIf there are even number of terms, then median is the average of(n/2)th term and [(n/2) + 1]th termFor grouped data, median is calculated by the following formula:Median = l + h × [(n/2) – cf]/fWhere,l = lower limit of median classn = number of observationscf = cumulative frequency of class preceding the median classf = frequency of median classh = 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

 Class Frequency Cumulative Frequency 10-15 8 8 15-20 6 14 20-25 4 18 25-30 7 25 30-35 5 30

• Q2

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

Marks:1

• Q3

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

Marks:1

• Q4

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

Marks:1

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

• Q5

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

Marks:1