Combined mean

2. COMBINED MEAN
A combined mean is a mean of two or more separate groups.
Example-01.
A distribution consists of 3 components with frequencies 45, 40 and
6, having their means 2, 2.5 and 2 respectively. Find mean of the
combined distribution.
1 2 3
1 2 3
1 1 2 2 3 3
1 2 3
45 40 65
2 2.5 2
45(2) 40(2.5) 65(2)
45 40 65
2.13
c
c
n n n
x x x
n x n x n x
x
n n n
x
= = =
= = =
+ +
=
+ +
+ +
=
+ +
=

3. Example-2:
The average wage of 10 men is Rs.50 per hour and the average wage of
further 15 men is Rs.60 per hour. Find the average wage of all men.
Solution:
Groups
1st
2nd
10
15
50
60
500
900
Sum 25 1400
Example-3:
The average wage of 10, 15 and 20 students is 60 kg, 50 kg and 68 kg
respectively. Find the average weight of the 45 students.
Solution:
Groups
1st
2nd
3rd
10
15
20
60
50
68
600
900
1360
Sum 45 2860
Kg
n x xn
56
25
1400
n
xn
xc ===


n x xn
56.63
45
2860
n
xn
xc ===



4. Example-4.
The average salary of male employees in a firm was Rs. 520 and that
of females was 420. The mean salary of all the employees was Rs.
500. Find the percentage of male and female employees.
Given that
500=cx
femalesofnonx
malesofnonx
.;420
;520
22
11
==
==
1 1 2 2
1 2
1 2
1 2
1 2 1 2
1 2 1 2
1 1 2 2
1 2
1
2
1
2
520 420
500
( )
500( ) 520 420
500 500 520 420
500 520 420 500
20 80
80
20
4
1
c
n x n x
x
n n
n n
n n
n n n n
n n n n
n n n n
n n
n
n
n
n
+
=
+
+
=
+
+ = +
+ = +
− = −
− = −
=
=
Hence the percentage of male employees =
4
100 80%
4 1
 =
+
and the percentage of female employees = %20100
14
1
=
+

5. Do yourself
1) The average wage of 4 men is Rs.17 per week. What is the
average wage of further 6 men if the average wage of all 10
men is Rs.20 (Answer = 22).
2) An average monthly production of a certain factory for the
first 9 months is 2584 units and for the remaining three
months it is 2416 units find average monthly production
(Answer = 2542).
3) Three sections of statistics class containing 28, 32 and 35
students Averaged83, 80 and 76 respectively, on the same
final examination. What is thecombined population mean for
all 3 sections? (Answer = 79.4)
4) A survey of a random sample of people leaving an
amusement park showed an average expenditure of $10.30
for the evening. The average expenditure for the 20 girls in
the sample was $9.70 and for the boys it was $11.10. How
many boys are there in the random sample?
(Answer = 15 boys)
5) An electronic firm has two divisions one having 150
employees the other 50 in the first the employees have an
average of Rs. 1350 per month, in the second Rs. 1750 per
month. Calculate the average salary for the entire firm.
(Answer = 1450)
6) If the mean income of 200 workers in a manufacturing plant
is Rs. 1200 and the mean income for the workers in a second
plant is Rs. 1500 and the mean of the combined total workers
is Rs.1340. How many workers are in the second’s plant?
(Answer = 175)

6. 7) 20 girls coming to an exhibition spent an average of Rs.30.75
on a particular day and the average amount spent by the boys
on the same day was Rs.36.25. The combined mean of the
expenditure of boy’s and girl’s was Rs.33.20.Calculate the
number of boys coming on that particular day to the
exhibition. (Answer = 16)