MEASURE OF CENTRAL TENDENCY ( MEDIAN) FOR STATISTICS O LEVEL/IGCSE

The median is defined as a value which divides the data set that have been ordered, into two

equal parts, one part compromising of observations greater than and the other part smaller than it.

Median=(n/2)th value ( for single set of observations)

Median= L+h/f(n/2-C) for frequency distribution

Note: For odd number of observations we use n+1 in the place of n, above mentioned formulas.

Example: find the median

3, 4, 5, 1, 6, 4,1,8

To find the median first we have to arrange it in ascending order

1,1,3,4,4,5,6,8

Solution:

Median=(8/2)th value

Median=4th value

Median=4

Median frequency distribution example

Class Intervals	Class Boundaries	Frequency	CF
16-19	15.5-19.5	2	2
20-23	19.5-23.5	8	10
24-27	23.5-27.5	18	28
28-31	27.5-31.5	15	43
32-35	31.5-35.5	6	49
36-39	35.5-39.5	1	50

Ef=50

Median value= 50/2= 25^th value

Median=L+h/f(n/2-C)

Median=23.5+4/18(25-10)

Median=26.83

Graphical Determination of the Median

1. With the help of cumulativee frequency curve

Median=n/2 where n=sum of all frequencies.

200/2=100th

Median is between 439.5 and 449.5. Median in statistics can also be called Q2 or Median Quartile.

Advantages of Median

1. It is easily calculated and understood
2. It is located even when the values are not capable of quantitative measurement.
3. It is not affected by extreme values
4. It can be located graphically
5. It can be easily located even if the class intervals in the series are unequal

Disadvantages of Median

1. It is not subjected to algebraic treatments.
2. It cannot be used in further statistical treatment
3. It does not have sampling stability
4. It does not take into account the values of all items in the series.

USES

• It is useful in those cases where numerical measurements are not possible.
• It is also useful in those cases where mathematical calculation cannot be made in order to obtain the mean.
• It is generally used in studying phenomenon like skills, honesty, intelligence etc.