Question

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

Answer 1

Answer :-

Mean = 54

Given :-

There are two groups containing 30 and 20 observation having 50 and 60 as arithmetic mean.

To find :-

The combined arithmetic mean.

Solution:-

Let the sum of observation of two groups be x and y Respectively.

→$\mathsf{Mean = \dfrac{\text{Sum of observation}}{\text{Total number of observation}}}$

A/Q

→$50 = \dfrac{x}{30}$

$x = 1500$

• Sum of observation is 1500.

→$60 = \dfrac{y}{20}$

$y = 1200$

• Sum of observation is 1200.

Combined arithmetic mean is given by :-

→$\overline {X} = \dfrac{\text{Total sum of observation}}{\text{Total number of observation}}$

→$\overline {X} = \dfrac{x+y}{30 + 20}$

→$\overline {X} = \dfrac{1500 +1200}{50}$

→$\overline{X}=\dfrac{2700}{50}$

→$\overline{X}= 54$

hence,

The combined arithmetic mean is 54.

Answer 2

Answer:

Mean = 54

Given :-

There are two groups containing 30 and 20 observation having 50 and 60 as arithmetic mean.

To find :-

The combined arithmetic mean.

Solution:-

Let the sum of observation of two groups be x and y Respectively.

→\mathsf{Mean = \dfrac{\text{Sum of observation}}{\text{Total number of observation}}}Mean=

Total number of observation

Sum of observation

A/Q

→50 = \dfrac{x}{30}50=

30

x

x = 1500x=1500

Sum of observation is 1500.

→60 = \dfrac{y}{20}60=

20

y

y = 1200y=1200

Sum of observation is 1200.

Combined arithmetic mean is given by :-

→\overline {X} = \dfrac{\text{Total sum of observation}}{\text{Total number of observation}}

X

=

Total number of observation

Total sum of observation

→\overline {X} = \dfrac{x+y}{30 + 20}

X

=

30+20

x+y

→\overline {X} = \dfrac{1500 +1200}{50}

X

=

50

1500+1200

→\overline{X}=\dfrac{2700}{50}

X

=

50

2700

→\overline{X}= 54

X

=54

hence,

The combined arithmetic mean is 54.