If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 13,

1.	If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 13, find the value of x and hence find the mean of the last three observations.
Answer» We know that Number of observations = 5 It is given that mean = 13 We can write it as [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)]/5 = 13 On further calculation 5x + 20 = 13 (5) So we get 5x + 20 = 65 By subtraction 5x = 45 By division x = 9 By substituting the value of x We know that the last three observations are 9 + 4 = 13 9 + 6 = 15 9 + 8 = 17 We know that Mean of last three observations = (13 + 15 + 17)/3 On further calculation Mean of last three observations = 45/3 By division Mean of last three observations = 15 Therefore, the mean of last three observations is 15.

If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 13, find the value of x and hence find the mean of the last three observations.

Answer»

We know that

Number of observations = 5

It is given that mean = 13

We can write it as

[x + (x + 2) + (x + 4) + (x + 6) + (x + 8)]/5 = 13

On further calculation

5x + 20 = 13 (5)

So we get

5x + 20 = 65

By subtraction

5x = 45

By division

x = 9

By substituting the value of x

We know that the last three observations are

9 + 4 = 13

9 + 6 = 15

9 + 8 = 17

We know that

Mean of last three observations = (13 + 15 + 17)/3

On further calculation

Mean of last three observations = 45/3

By division

Mean of last three observations = 15

Therefore, the mean of last three observations is 15.

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