Median of Ungrouped Data

INTRODUCTION

Ungrouped data:

The data present in its original form is known as ungrouped data . ungrouped data is nothing but raw data.

Median:

Median is the center value of the distribution.  That is median of a distribution is the value of the variable which divides it into two equal parts. It is the value of the variable such that the number of observations above it is equal to the number of observations below it.

Finding Median of Ungrouped Data :

Steps to find the median of ungrouped data :

To find the median of ungrouped data arrange the given values in ascending order

If the number of observations n is odd,

The median is  `(n+1)/2` st value.

If the number of observations is even,

Median =   ( `n/2` th value + `n/2` +1th value) / 2    (the average of the two middle values)

Example Problems on Finding Median of Ungrouped Data :

Example for Even number of observations:

Consider an example problem ,

Peter  scored 7,9,5,3,15 and 16 points in 6 basketball games. he wants to show that he is a valuable player. Find the median of his data .

Median – Median is the middle number of the given set  of numbers

Solution :

Arrange the numbers in order from lowest to highest.

That would be: 3, 5, 7, 9, 15, 16

There is an even number of numbers (6 total). Since there is no middle number, And the formula to find the median of  even number of observations is ,

Median = (n/ 2 )+ ((n/2 ) +1) /2

Where , n= no.of observations

Hence ,

Median = (6/2 + 6/2 +1 ) /2

Average of 3rd and 4th  numbers

Which is     ->  (7+9 )/ 2

= 16/2

= 8

Median of ungrouped data  3, 5, 7, 9, 15, 16 = 8

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Example for odd no.of observations:

A volley ball team had scores of 383, 392, and 401 strokes in a tournament. The minimum score wins. The team wants to show that it played well. Find the median?

Solution:

Here total number of observations = 3 (which is odd)

Formula to find median = (n+1)/2 th observation

Median = 3+1 / 2

= 4/2

=2

The median is 2nd number . Hence,

Median of ungrouped data 383, 392, 401 is 392.