Question

Find the sum of the deviations of all observation of the data 5,8,10,15,22 from their mean.​

Answer 1

Correct answer:-

5, 8, 1, 15, 22

Moon = sum of observation

__________________

no. of obesuation

=5+8+10+15+22/5.

= 60/5.

=12.

Therefore, Sum of deviations -

=∣5−12∣+∣8−12∣+∣10−12∣+∣15−12∣+∣22−12∣

=∣7∣+∣−4∣+∣−2∣+∣3∣+∣10∣

=7+4+2+3+10

=26 [Ans].

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Answer 2

Statistics

The given observations of the data are 5, 8, 10, 15, 22 and the Number of observations is 5. With this information, we have been asked to find out the sum of the deviations.

We know the airthmetic mean of sum of observations and number of observations is,

$\boxed{\bf{Mean = \dfrac{Sum \: of \: the \: observations}{Number \: of \: observations}}}$

Substituting the given values in it, we get:

$\implies Mean = \dfrac{5 + 8 + 10 + 15 + 22}{5} \\ \\ \implies Mean = \dfrac{60}{5} \\ \\ \implies Mean = 12$

Now, Sum of the deviations;

$\implies | 5 - 12 | + | 8 - 12 | + | 10 - 12 | + | 15 - 12 | + | 22 - 12 | \\ \\ \implies | - 7 | + | -4 | + | -2 | + | 3 | + | 10 | \\ \\ \implies 7 + 4 + 2 + 3 + 10 \\ \\ \implies \boxed{\bf{26}}$

Hence, the sum of the deviations is 26.