Question

. If sum of squares of the values = 3390, N = 30 and standard deviation = 7, find out the mean.​

Answer 1

Step-by-step explanation:

49=3390/30 -m2

49=113-m2

m2=113-49

=64

${7}^{2} = 3390 \div 30 - {m}^{2} \\ 49 = 113 - {m }^{2} \\ {m }^{2} = 113 - 49 = \sqrt{64} \\ = 8 \: ans$

Answer 2

Answer:

The mean of the given data is 8

Step-by-step explanation:

Given that,

Sum of squares of values of a certain sample is 3390

No.of observations in the sample is $N=30$

Hence we can write

$\Sigma X^{2}=3390-- > (1)$

The mean of the data is $\bar{X}=\frac{x_{1}+x_{2}+.....+x_{30}}{30}$

Also given that,the standard deviation of the data is 7

$= > \sigma =7$

The relation between standard deviation,mean of the data and sum of squares of the term is shown below.

$\sigma^{2}=\frac{\Sigma X^{2}}{N} -\bar{X}^{2}$

Substituting the known values in above relation,we get

$7^{2} =\frac{3390}{30} -\bar{X}^{2}\\= > 49=113-(\bar{X})^{2}= > (\bar{X})^{2}=113-49=64= > \bar{X}=8$

Therefore,The mean of the given data is 8

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