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The mean of five observations is 15. If the mean of first three observations is 14 and that of last three is 17, then the third observation is
- a)29
- b)31
- c)32
- d)18
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
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
=93−75
=18
Most Upvoted Answer
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 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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Community Answer
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.
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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The mean of five observations is 15. If the mean of first three observations is 14 and that of last three is 17, then the third observation isa)29b)31c)32d)18Correct answer is option 'D'. Can you explain this answer?
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