The mean of five observations is 15. If the mean of first three observ...
⇒ It is given that Mean of 5 observations is 15.
∴ The sum of observations =15×5=75.
∴ It is given that mean of the first 3 observations is 14.
∴ The sum of first three observations =14×3=42.
⇒ Given that mean of the last 3 observations is 17.
∴ The sum of the last three observations =17×3=51
∴ The third observation =(42+51)−75
=93−75
=18
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The mean of five observations is 15. If the mean of first three observ...
It is given that Mean of 5 observations is 15.
∴ The sum of observations =15×5=75.
∴ It is given that mean of the first 3 observations is 14.
∴ The sum of first three observations =14×3=42.
⇒ Given that mean of the last 3 observations is 17.
∴ The sum of the last three observations =17×3=51
∴ The third observation =(42+51)−75
=93−75
=18
The mean of five observations is 15. If the mean of first three observ...
Given:
Mean of 5 observations = 15
Mean of first three observations = 14
Mean of last three observations = 17
To find: Third observation
Solution:
Let the five observations be a, b, c, d, and e.
Mean of 5 observations = (a + b + c + d + e)/5 = 15
=> a + b + c + d + e = 75 ---(1)
Mean of first three observations = (a + b + c)/3 = 14
=> a + b + c = 42 ---(2)
Mean of last three observations = (c + d + e)/3 = 17
=> c + d + e = 51 ---(3)
Adding equations (2) and (3), we get:
a + b + 2c + d + e = 93 ---(4)
Subtracting equation (2) from equation (1), we get:
d + e = 33 ---(5)
Subtracting equation (3) from equation (1), we get:
a + b = 24 ---(6)
Adding equations (5) and (6), we get:
a + b + d + e = 57
Substituting this value in equation (4), we get:
57 + 2c = 93
=> 2c = 36
=> c = 18
Therefore, the third observation is c, which is equal to 18.
Hence, the correct option is (d) 18.
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