Question

The mean of 10 observations is 14.4. Out of these mean of 4 observations is 16.5, then find the mean of remaining observations: (a) 13.6 (b) 13 (c) 13.8 (d) 12

Answer 1

Answer:13

Step-by-step explanation:see sttachement

Answer 2

Given,

The mean of 10 observations = 14.4

Out of these, mean of 4 observations = 16.5

To find,

The mean of the remaining observations.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the 10 observations are X1, X2, -------X9, and X10, respectively.

Mathematically,

The mean of a set of given data can be calculated as follows;

The mean = (sum of all the observations)/(total number of observations)

{Statement-1}

Now, according to the question;

The mean of 10 observations = 14.4

=> (sum of all the 10 observations)/(total number of observations) = 14.4

=> (X1 + X2 +------+ X9 + X10)/10 = 14.4

=> (X1 + X2 +------+ X9 + X10) = 144

{Equation-1}

And, the mean of 4 observations = 16.5

=> (sum of all the 4 observations)/4 = 16.5

=> sum of all the 4 observations = 16.5×4 = 66

=> sum of all the 4 observations = 66

{Equation-2}

Now, according to the question;

The sum of the remaining 6 observations

= (sum of all the 10 observations) - (sum of all the 4 observations)

= 144-66

{according to equation-1 and equation-2}

= 78

So, the mean of the remaining 6 observations

= (sum of the remaining 6 observations)/6

{according to statement-1}

= 78/6 = 13

Hence, the mean of the remaining 6 observations is equal to 13.