Question

A set of 10 values has arithmetic mean
20 find the new arithmetic mean if one of
the observations equal to 5 is replaced
by 10.​

Answer 1

Given,

Arithmetic means of 10 values = 20

To Find,

The new arithmetic mean if one of the observations equal to 5 is replaced by 10.

Solution,

Since the mean of 10 values is equal to 20.

(x₁+x₂+...+5)/10 = 20

x₁+x₂+...+5 = 200

x₁+x₂+...x₉ = 195

Now,

New mean = (x₁+x₂+...+10)/10

                   = (195+10)/10

                    = 205/10

Hence, the new mean is equal to 20.5

Answer 2

The new arithmetic mean = 20.5

Given :

• A set of 10 values has arithmetic mean 20

• One of the observations equal to 5 is replaced by 10.

To find :

The new arithmetic mean

Solution :

Step 1 of 3 :

Write down sum of the observations

Here it is given that a set of 10 values has arithmetic mean 20

Number of observations = 10

Sum of the observations

= 10 × 20

= 200

Step 2 of 3 :

Calculate the new sum of observations

It is given that one of the observations equal to 5 is replaced by 10.

Thus the new sum of observations

= 200 - 5 + 10

= 205

Step 3 of 3 :

Find new arithmetic mean

The new arithmetic mean

$\displaystyle \sf{ = \frac{Sum \: of \: the \: observations}{Number \: of \: observations} }$

$\displaystyle \sf{ = \frac{205}{10} }$

$\displaystyle \sf{ = 20.5}$

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