Find the missing frequency if arithmetic mean is 28 of the data given below and find
median of the series later.
C-10
10-20
20-30
30–40
40-50
50-60
no. of shop
12
18
27
_
17
6
Answers
Answer:
Let the missing frequency be x
Arithmetic mean = 28 (given)
X | Frequency(f) | Mid value (m) | fm
0-10 | 12 | 5 | 60
10-20 | 18 | 15 | 270
20-30 | 27 | 25 | 675
30-40 | x | 35 | 35(x)
40-50 | 17 | 45 | 765
50-60 | 6 | 55 | 330
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| Σf = 80+x | | Σfm = 2100+35 x
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Mean = Σfx/Σf
⇒ 28 = 2100 + 35x/80 + x
⇒ 2240 + 28x = 2100 + 35
⇒ 2240 - 2100 = 35x - 25x
⇒ 140 = 7x
⇒ x = 140/7 = 20
Missing frequency = 20
Class Interval | Frequency | Cumulative frequency
| (f) | (CF)
0-10 | 12 | 12
10-20 | 18 | 30
20-30 | 27 | 57
30-40 | x | 77
40-50 | 17 | 94
50-60 | 6 | 100
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Total | Σf = 100 |
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Median = Size of (N/2)th item
= 100/2 = 50th item
It lies in class 20-30.
