HOW TO FIND COMBINED MEAN FROM WORD PROBLEMS

Problem 1 :

Find Combined Mean from the following data

n₁= 40, x₁ = 10

n₂ = 60, x₂ = 15

Solution :

The combined mean is 13.

Problem 2 :

60 students of section A of Class XI, obtained 40 mean marks in statistics, 40 students of section B obtained 35 mean marks in statistics. Find out mean marks in Statistics for class XI as a whole.

Solution :

By observing the information,

Number of students in section A, n₁= 60

Mean of section A, x₁ = 40

Number of students in section B, n₂ = 40

Mean of section B, x₂ = 35

So, the mean mark is 38.

Problem 3 :

The mean monthly salary paid to all employees in a certain company was $600. The mean monthly salaries paid to male and female employees were $620 and $520 respectively. Find the percentage of male to female employees in the company.

Solution :

Combined mean = 600

Let n₁ and n₂ be the number of male and female employees respectively.

x₁ and x₂ are mean wages.

x₁ = 620 and x₂ = 520

Percentage of male employees = (4/5) x 100%

= 80%

Percentage of female employees = (1/5) x 100%

= 20%

Problem 4 :

The mean salary for a group of 40 female workers is $5200 per month and that for a group of 60 male workers is $6800 per month. What is the combined mean salary ?

Solution :

n₁= 40, x₁ = 5200

n₂ = 60, x₂ = 6800

So, the combined mean salary is 6160.

Problem 5 :

The average salary of a group of unskilled workers is $10000 and that of a group of skilled workers  is $15000. If the combined salary is $12000, then what is the percentages of skilled workers ?

Solution :

Combined mean salary = 12000

Let n₁ and n₂ be the number of unskilled and skilled workers respectively.

x₁ and x₂ are mean wages.

x₁ = 10000 and x₂ = 15000

Percentage of unskilled workers = 3/5 x 100%

= 60%

Percentage of skilled workers = 2/5 x 100%

= 40%

So, the answer is 40%.

Problem 6 :

If there are two groups containing 30 and 20 observations and having 50 and 60 arithmetic means, then the combined arithmetic mean is.

a)  55     b)  56     c)  54    d) 52

Solution :

n₁= 30, x₁ = 50

n₂ = 20, x₂ = 60

So, combined arithmetic mean is 54.