Math, asked by vinayak1894, 9 months ago

If the mean of the observation:x,x+3,x+5,x+7,x+10 is 9, then find the mean of the last three observations.

Answers

Answered by sourya1794
63

Given :-

  • The mean of the observation x, x+3, x+5, x+7, x+10 is 9.

To find :-

  • The mean of last three observation.

Solution :-

we know that,

\green{\bigstar}\:\:{\underline{\boxed{\bf\pink{Mean=\dfrac{Sum\:of\:observation}{Number\:of\:observation}}}}}

\rm\:mean=\dfrac{x+(x+3)+(x+5)+(x+7)+(x+10)}{5}

\rm\longrightarrow\:mean=\dfrac{5x+25}{5}

\rm\longrightarrow\:mean=\dfrac{\cancel{5}(x+5)}{\cancel{5}}

\rm\longrightarrow\:mean=x+5

Now,

From the above observation,

  • Mean = 9 (given)

∴ x + 5 = 9

x = 9 - 5

x = 4

last three observation (x + 5), (x + 7), (x + 10)

(4 + 5), (4 + 7), (4 + 10)

9, 11, 14

So, last three observation will be 9, 11, 14

Then,

\rm\:Mean\:of\:last\:three\:observation=\dfrac{9+11+14}{3}

\rm\:Mean\:of\:last\:three\:observation=\dfrac{34}{3}

\rm\:Mean\:of\:last\:three\:observation=11\dfrac{1}{3}

Hence,the mean of last three observation will be 11 ⅓.

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