Question

The mean of 5 observations x, x+4, x+8, x+12 and x+16 is 13. then find the observations. ​

Answer 1

SOLUTION:

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GIVEN:

The mean of 5 observations x, x+4, x+8, x+12 and x+16 is 13.

TO FIND:

Then find the observations.

STEPS TO DO:

$\sf Mean = \dfrac{sum \: of \: observations }{ no \: of \: observations}$

x + x+4 + x+8 + x+12 + x+16 / 5 = 13

5x + 40 / 5 = 13

5x + 40 = 13 × 5

5x + 40 = 65

5x = 65 - 40

5x = 25

x = 25/5

x = 5

HENCE:

The 5 observations are:

1st observation = x = 5

2nd observation = x + 4 = 5 + 4 = 9

3rd observation = x + 8 = 5 + 8 = 13

4th observation = x + 12 = 5 + 12 = 17

5th observation = x + 16 = 5 + 16 = 21

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Answer 2

Given that,

• The mean of 5 observations are x, x+4, x+8, x+12, x+16 is 13.

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Here,

• Sum of observations = 13
• Number of observations = 5

$☯︎\sf\underline{Using \: mean \: formula \: - }$

$\boxed{\boxed{\bold\purple{\bigstar \: mean \: = \frac{sum \: of \: observations}{number \: of \: observations} }}}$

$\sf\implies \: mean \: = \frac{x + x + 4 + x + 8 + x + 12 + x + 16}{5} \\ \\ \sf\implies \: 13 = \frac{x+ x + 4 + x + 8 + x + 12 + x + 16}{5} \\ \\ \sf\implies \: 16 = \frac{5x + 12 + 12 + 16}{5} \\ \\ \sf\implies \: 16 = \frac{5x + 24 + 16}{5} \\ \\ \sf\implies \: 13 = \frac{5x + 40}{5} \\ \\ \sf\implies \: 13 \times 5 = 5x + 40 \\ \\ \sf\implies \: 65 = 5x + 40 \\ \\ \sf\implies \: 65 - 40 = 5x \\ \\ \sf\implies \: 25= 5x \\ \\ \sf\implies \: x = \cancel \dfrac{25}{5} \\ \\ \sf\implies \: x = \boxed{\sf\purple{5}}\bigstar$

Now,

• $\sf \: 1st \: observation \: x \: = \bold{5}$
• $\sf \: 2nd \: observation \: 5 + 5 = 5 + 4 = \bold{9}$
• $\sf \: 3rd \: observation \: x + 8 = 5 + 8 = \bold{13}$
• $\sf \: 4th \: observation \: x + 12 = 5 + 12 = \bold{17}$
• $\sf \: 5th \: observation \: x + 16 = 5 + 16 = \bold{21}$

$\sf\therefore\underline{Hence, \: the \: observations \: are \: \bold{5, \: 9, \: 13, \: 17 \: and \: 21} \: respectively}$