Question

The mean of 10 observations is 5.5, when one new observation is included in the data set, the mean of the observations becomes 6.0. What is the value of new observation that was added to the dataset?

Answer 1

let A= the new observation added

X=Sum of all observation in first case

by given data,

5.5= X/10

so, X is 5.5×10=55...........eq 1

6=(X+A)/10

so, A= 60- X

by eq 1,

A=60-55

A=5

Answer 2

Answer:

The required value of the new observation added is 11

Step-by-step explanation:

It is given to us that :

the mean of 10 observations = 5.5

Now, the total sum of the 10 observations = 5.5 x 10 = 55

Let the new observation added be "x"

Therefore, (total sum of 10 observations) + x = 6

                                        10 + 1

or, (total sum of 10 observations) + x = 6

                             11

or, 55 + x = 6 x 11

or, x = 66 - 55 = 11

Hence,  the required value of the new observation added is 11

Mean : In terms of statistics, the mean is defined as one of the central tendency and it defines the ratio of the summation of the observations to the number of observation given.

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