Question

The mean of 10 observations is 25.6. Including one new observation,the mean of all the observations together is 26. Find the newly included observations​

Answer 1

Given :

• Mean of the 10 observations = 26.5
• Mean after new observation is added = 26

To Find :

• What is the newly added observation?

Let's Assume :

Let's Assume that, the newly added observations is 'x'

So, we will calculate the other quantities with the help of this variable

Solution :

Given, Mean of ten observations = 26.5

$\displaystyle \rm \implies \frac{total \: sum}{10} = 26.5$

$\implies \displaystyle \rm total \: sum = 26.5 \times 10$

$\implies \displaystyle \rm total \: sum = 265$

So, the total sum of first 10 observations = 265

Now, if the 11th observations (x) is added, the sum will be :

265+x

So, the new Mean will be :

$\implies \displaystyle \rm mean = \frac{265 + x}{11}$

$\displaystyle \rm \implies \frac{265 + x}{11} = 26$

$\displaystyle \rm \implies {265 + x} = 26 \times 11$

$\displaystyle \rm \implies {265 + x} = 286$

$\displaystyle \rm \implies x = 286 - 265$

$\red{ \underline{ \boxed{\displaystyle \rm \implies x = 21}}}$

So, the new observation = 21

Final Answer :

We got that :

• The newly added observation = 21

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Additional Information:

• Mean : Mean is a central tendency of a set of observations, which is the total sum of observations divided by total number of observations.

Mean = (Total sum of Ob.) ÷ total number of ob.

• Median : The central most value of a set when arranged in Ascending or descending order

• Mode : The most occurred element in a set of observations is called the mode of the set