Question

A group of 20 observations has arithmetic mean 100. If each observation is doubled the mean will be​

Answer 1

Answer:

Step-by-step explanation:

AM=100

so sum=100*20=2000

Now each observation is doubled

So sum will be=2*2000=4000

thus AM=4000/20

=200

Answer 2

Given,

The Arithmetic Mean of a group of 20 observations = 100

To find,

The value of the Arithmetic Mean when each observation is doubled.

Solution,

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

Mathematically,

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

The arithmetic mean (A.M.)

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

{Statement-1}

Let us assume that the 20 observations given in the question are X1, X2, -----X20.

Now, according to the question and statement-1;

The Arithmetic Mean of the group of 20 observations = 100

=> (sum of all the observations)/(total number of observations) = 100

=> (X1 + X2 + ----- + X19 + X20)/20 = 100

=> (X1 + X2 + ----- + X19 + X20) = 2000

{Equation-1}

Now, when each of the given observation is doubled, the set of 20 observations become 2X1, 2X2, -----2X19, 2X20.

Now, according to the question and statement-1;

The Arithmetic Mean of the group of 20 doubled observations

= (2X1 + 2X2 + ----- + 2X19 + 2X20)/20

= 2/20 × (X1 + X2 + ----- + X19 + X20)

= 1/10 × 2000 {according to equation-1}

= 200

Hence, the Arithmetic Mean of the group of 20 doubled observations is equal to 200.