Example: From the following data, calculate the median and the first and third quartile wages:
|
Weekly
wages ($) |
No. of |
Weekly |
No. of |
|
30—32 |
2 |
40—42 |
62 |
|
32—34 |
9 |
42—44 |
39 |
|
34—36 |
25 |
44—46 |
20 |
|
36—38 |
30 |
46—48 |
11 |
|
38—40 |
49 |
48—50 |
3 |
Solution: Computation of Median and Quartiles
|
Weekly
wages (Rs.) |
No. of workers (f) |
Cumulative
frequency |
|
30—32 |
2 |
2 |
|
32—34 |
9 |
11 |
|
34—36 |
25 |
36 |
|
36—38 |
30 |
66 |
|
38—40 |
49 |
115 |
|
40—42 |
62 |
177 |
|
42—44 |
39 |
216 |
|
44—46 |
20 |
236 |
|
46—48 |
11 |
247 |
|
48—50 |
3 |
250 |
|
|
N—250 |
|
Median is the value of (250/2) th or 125th item which lies in the 40—42 group. Its value would be M = l2 + (l2-l1)/f1 (m-c)
= 40+ 2/62 (125—115) =40.32
Lower Quartile is the value of (250/4) th or 62.5th item which lies in 36—38 group. Its value would be Q1 = l1+ (l2-l1)/f1 (q1—c) where q1 is the quartile number or 62.5 = 36 + (38-36)/ 30 (62.5-36) =-37.75
Upper Quartile is the value of (3(N))/4th or 187.5th item which lies in 42—44 group. Its value would be,42+ (44-42) * 187.5-177)/39 =42.54