Question

If the mean of the observations x, x+2, x+4 , x+6 and
x+8 is 11. Find:
i. the value of x
ii. the mean of the first 3 observations

Answer 1

Step-by-step explanation:

Given :

Mean of the observations (x) , (x + 2) , (x + 4) , (x + 6) and (x + 8) is 11.

To find :

The value of x.

The mean of the first 3observations.

Solution :

Mean can be found using the formula,

• Sum of all observations ÷ Number of observations

Substituting the values,

• (x) + (x + 2) + (x + 4) + (x + 6) + (x + 8)/5 = 11
• (5x + 20)/5 = 11
• 5x + 20 = 11 × 5
• 5x + 20 = 55
• 5x = 55 - 20
• 5x = 35
• x = 35/5
• x = 7

∴ Value of x is 7.

Mean of first 3 observations,

• (x) + (x + 2) + (x + 4)/3

Substituting the value of x,

• (x) + (x + 2) + (x + 4)/3
• (3x + 6)/3
• (3(7) + 6))/3
• (21 + 6)/3
• 27/3
• 9

∴ Mean of first 3 observations is 9.

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Answer 2

x, x+2, x+4 , x+6 and  x+8 = obs

mean = 11

mean = sum of obs/total obs

total obs = 5

so, x, x+2, x+4 , x+6 and  x+8/5 = 11

5x = 35

x = 7

mean of first 3 obs =

(x) + (x + 2) + (x + 4)/3

keep x value 7

27/3

9.