Question

The mean of 10 numbers is 8.if an eleventh number is included in the data'the mean become 9. what is the eleventh number​

Answer 1

Answer:

Eleventh number is 19.

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Step-by-step explanation:

No. of observations = 10

Mean = 8

Therefore, sum of observations = 10 × 8 = 80

When one number is included,

No. of observations = 11

Mean = 9

Therefore, sum of observations = 11 × 9 = 99

Therefore, finally, eleventh(included) number =

99 - 80 = 19

Answer 2

Given :  The mean of 10 numbers is 8.

an eleventh number is included in the data  the mean become 9.  

To Find : the eleventh number​

Solution:

$\[\begin{align} & Mean=\frac{\text{sum of all the obervations}}{\text{number of the observations}} \\ & Mean=\overline{x}=\frac{\sum\limits_{i=1}^{n}{{{X}_{i}}}}{n} \\ & Mean=\overline{x}=\frac{\sum fx}{\sum f} \\ & Mean=\overline{x}=A+\frac{\sum fd}{\sum f} \\& Mean=\overline{x}=A+h \times \frac{\sum fu}{\sum f} \\\end{align}\]$$\[\begin{align} & Mean=\frac{\text{sum of all the obervations}}{\text{number of the observations}} \\ & Mean=\overline{x}=\frac{\sum\limits_{i=1}^{n}{{{X}_{i}}}}{n} \\ & Mean=\overline{x}=\frac{\sum fx}{\sum f} \\ & Mean=\overline{x}=A+\frac{\sum fd}{\sum f} \\& Mean=\overline{x}=A+h \times \frac{\sum fu}{\sum f} \\\end{align}\]$$Mean=\frac{\text{sum of all the obervations}}{\text{number of the observations}} \\ Mean=\overline{x}=\frac{\sum\limits_{i=1}^{n}{{{X}_{i}}}}{n}$

The mean of 10 numbers is 8.

Sum of all 10 numbers   = 10 * 8  = 80

The mean of 11 numbers is 9.

Sum of all 11 numbers   = 11 * 9  =  99

eleventh number = 99 - 80

=> eleventh number = 19

Hence eleventh number​ included is  19

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