THIS DISCUSSES THE MEDIAN OF MEASURES OF CENTRAL TENDENCY IN STATISTICS. The median is the middle number in a sorted, ascending or descending, list of numbers. If there is an odd number of numbers, the median value is the number that is in the middle, with the same number of numbers below and above. If there is an even number of numbers in the list, the middle pair must be determined, added together, and divided by two to find the median value. To find the median value in a list with an even number of numbers, one must determine the middle pair, add them, and divide by two. Again, arrange the numbers in order from lowest to highest.

1. MEASURES OF CENTRAL TENDENCY
MEDIAN
“condensation of a large amount of data into a single value is known as measures of central tendency.”
Prepared by : FAIROOS AHMED

2. ● Median is a statistical measure that determines the middle value of a dataset listed in
ascending order.
● It denotes a value or quantity lying at the midpoint of a frequency distribution of observed
values or quantities, such that there is an equal probability of falling above or below it.
● The median is the middle number in a sorted, ascending or descending, list of numbers.
○ To determine the median value in a sequence of numbers, the numbers must first be
sorted, or arranged, in value order from lowest to highest or highest to lowest.
● If there is an odd amount of numbers, the median value is the number that is in the middle,
with the same amount of numbers below and above.
● If there is an even amount of numbers in the list, the middle pair must be determined,
added together, and divided by two to find the median value.

3. ● the median is not affected by extreme values
● For Example :
○ Data Set :
■ 3, 13, 2, 34, 11, 17, 27,
● Arrange the data in Ascending / Descending Order
○ Ascending Order : 2, 3, 11, 13, 17, 27, 34
○ Descending Order : 34, 27, 17, 13, 11, 3, 2
● Find the middle value. ( for ODD amount of numbers )
○ Ascending Order : 2, 3, 11, 13, 17, 27, 34
○ Descending Order : 34, 27, 17, 13, 11, 3, 2
● So the MEDIAN is “ 13 ”.

4. ● For EVEN amount of numbers
○ Data Set…. : 3, 13, 2, 34, 11, 26, 47
○ Arrange the data in Ascending / Descending Order.
■ Ascending Order : 2, 3, 11, 13, 17, 27, 34, 47
■ Descending Order : 47, 34, 27, 17, 13, 11, 3, 2
● Median is the average of the two numbers in the middle.
○ Determine the Middle Pair, add them, and divide by two.
● Middle Pair of given data set : 47, 34, 27, 17, 13, 11, 3, 2
○ Find the average : 17 + 13 / 2
■ = 30 / 2 = 15
○ Here the Median is 15.

5. FORMULA
● Let’s consider a data set with n observations.
○ If n is odd, then
■ MEDIAN =
● Eg :
○ Data Set : 2, 3, 4, 5, 6 , 7, 8
○ Here N = 7
○ N + 1 = 8
○ 8 / 2 = 4
○ 4th term in the data set is the median.
■ It is 5.
( N + 1) TH
2
Term.

6. ● If N is even, then
● Median =
● Eg: 142, 140, 130, 150, 160, 135, 158, 132
● Arrange the data in Ascending / Descending Order
○ Ascending Order : 130, 132, 135, 140, 142, 150, 158, 160
○ Count the Number of Observation = 8
● Median = (8/2)th item + (8/2)+1th item 4th item + 5 th item
140+142
2
2 =
2
= 2
= 141
MEDIAN = 141

7. FOR CONTINUOUS SERIES
Median Class = find N/2 . see where the number falls. That's the median class.
N = Sum total of Frequencies or Cumulative Frequency
i= class interval
i
i

9. For discrete series

10. For discrete series
So Median for this series is 30. M = 30

11. THANK YOU.