1. Basic Tools For Economic Analysis Cont’d.
Finding Median from A Grouped Frequency Distribution.
Median for a Grouped frequency distribution is calculated using the formula below:
Me=L1+(N/2-Fo)c
Fe Where
L1= the value of the lower class boundary of the median class;
N=total number of items
Fo= Cumulative frequency of the class just above the one containing the median
Fe=Frequency of the median class
C= Class size
Eg. Use the table below to calculate the median mark.

2. Median from a grouped frequency distribution
Class interval
frequency
Class boundary
Cumulative frequency
1-10 6
11-20 8 14
21-30 20
31-40 4 24
41-50 28

3. From table above N=28, L1=10.5, C=10, Fe=8, Fo=6 Substituting we have
Median= Me=L1+(N/2-Fo)c Fe
Me=10.5+(28/2-6)10 8
=10.5+(14-6)10 =
Median=20.5
The Median mark is 20.5 ans

4. Advantages of Median -The median could be determined by observation
-It can be obtained graphically
-It is easy to understand
-It is easy to compute
-It is not affected by extreme values
Disadvantages of Median
-It ignores extreme values
-It is usually not representative of all values in distribution
-It is not easy to arrange the data in order of magnitude when large population is involved

5. The Mode Mo=L1+ (F1-F0)c F1-F0+F1-F2 Where Mo= Mode
The mode is the most frequent recurring number in a set of data. That is the number or value with the highest frequency
1)Eg. Find the mode of the following distribution:
3, 4, 5, 6, 9, 4, 6, 6, 7, 4,
From the above numbers, the mode is 6. ie 6 has the highest appearance.
2) Finding mode using calculation method
Mode can be calculated using the formula
Mo=L1+ (F1-F0)c
F1-F0+F1-F2
Where Mo= Mode
L1=Lower class boundary of the modal class
C= Class size
F1= frequency of the modal group
F0= frequency of the pre modal group
F2= frequency of the post modal group

6. Mode continued Eg. Consider the distribution below Class Boundary
Frequency 5 7
9---F0
12---F1
9---F2 6 3

7. Mode continued In calculating we use Mo=L1+(F1-F0/F1-F2+F1-F2)C
L1=29.5, F1=12, F0=9, F2=9, C=10
So,
Mo= 29.5+(12-9/ )10
= 29.5+(3/3+3)10
29.5+(3/6)10
=29.5+(30/6)
=29.5+5
=34.5 ans

8. Assignment 1) Compare and contrast median and mode
2)Find the mode of the following
a) 5, 7, 4, 5, 9, 4, 7, 8
b) 2, 4, 8, 5, 4, 3, 6, 7, 4, 2, 8, 4, 3, 5, 4, 2, 4.