Page 107 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes Alternative Method
N 95
47.5. Looking at the frequency distribution we note that there are 48 observations
2 2
which are less than or equal to 12 and there are 72 (i.e., 95 – 23) observations which are greater
than or equal to 12. Hence, median is 12.
Locate median of the following frequency distribution:

X : 0 1 2 3 4 5 6 7
f : 7 14 18 36 51 54 52 20
Solution:

X 0 1 2 3 4 5 6 7
f 7 14 18 36 51 54 52 20
c. f. 7 21 39 75 126 180 232 252
Here N = 252, i.e., even.

N 252 N
Now = = 126 and + 1 = 127.
2 2 2
Median is the mean of the size of 126th and 127th observation. From the table we note that
126th observation is 4 and 127th observation is 5.
4 +5
M = = 4.5
d 2
Alternative Method
Looking at the frequency distribution we note that there are 126 observations which are less
than or equal to 4 and there are 252 – 75 = 177 observations which are greater than or equal to 4.
4 5
Similarly, observation 5 also satisfies this criterion. Therefore, median 4.5.
2

When grouped frequency distribution is given (Interpolation formula)

The determination of median, in this case, will be explained with the help of the following
example.

Example: The following table shows the daily sales of 230 footpath sellers of Chandni
Chowk:

in
Sales ( ) : 0-500 500-1000 1000-1500 1500-2000
No . Sellers : 12 18 35 42
of
Sales ( ) : 2000-2500 2500-3000 3000-3500 3500-4000
in
of
No . Sellers : 50 45 20 8
Locate the median of the above data using
(i) only the less than type ogive, and
(ii) both, the less than and the greater than type ogives.

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