Question

Question : The mean of 5 observations is 15. If mean of first three observations is 14 and that of last three is 17, find the third observation.

Topic : Statistics
Class : 9th​

Answer 1

Answer:

Third observation = 18

Step-by-step explanation:

Let the observations be a, b, c, d, and e.

Then, according to the Question,

Mean of 5 observations = 15

(a + b + c + d + e)/5 = 15

a + b + c + d + e = 5 × 15

a + b + c + d + e = 75 ------ 1

Again, given,

Mean of first three observations = 14

(a + b + c)/3 = 14

a + b + c = 3 × 14

a + b + c = 42 ------ 2

Again, given,

Mean of last three observations = 17

(c + d + e)/3 = 17

c + d + e = 3 × 17

c + d + e = 51 ------- 3

Now, adding eq.2 and eq.3,

(a + b + c) + (c + d + e) = 42 + 51

a + b + c + c + d + e = 93

Since, Addition is Associative,

(a + b + c + d + e) + c = 93

But from eq.1 we get,

(a + b + c + d + e) + c = 93

(75) + c = 93

Now, solving for c,

75 + c = 93

c = 93 - 75

c = 18

Hence,

The third observation = 18

Hope it helped and believing you understood it. All the best.