If the arithmetic mean of the data given below is 28, find (a) the missing frequency, and (b) the median of the series:
|
Profit per retail shop (in Rs) |
0 – 10 |
10 – 20 |
20 – 30 |
30 – 40 |
40 – 50 |
50 – 60 |
|
Number of retail shops |
12 |
18 |
27 |
– |
17 |
6 |
(i) Let the missing frequency be f1
Arithmetic Mean = 28
|
Profit per Retail Shop (in Rs) |
No of Retail Shops |
Mid Value |
|
|
Class Interval |
(f) |
(m) |
fm |
|
0 – 10 |
12 |
5 |
60 |
|
10 – 20 |
18 |
15 |
270 |
|
20 – 30 |
27 |
25 |
675 |
|
30 – 40 |
f1 |
35 |
35f1 |
|
40 – 50 |
17 |
45 |
765 |
|
50 – 60 |
6 |
55 |
330 |
|
|
|
|
|
or, 2240 + 28f1 = 2100 + 35f1
or, 2240 – 2100 = 35f1 – 28f1
or, 140 = 7f1
f1 = 20
(ii)
|
|
Class Interval |
Frequency
(f) |
Cumulative Frequency (CF) |
|
|
0 – 10 |
12 |
12 |
|
|
10 – 20 |
18 |
30 |
|
|
20 – 30 |
27 |
57 |
|
|
30 – 40 |
20 |
77 |
|
|
40 – 50 |
17 |
94 |
|
|
50 – 60 |
6 |
100 |
|
|
Total |
|
|
So, the Median class = Size of 
item
= 50th item
50th item lies in the 57th cumulative frequency and the corresponding class interval is 20 – 30.
