Question

MEAN OF 25 OBSERVATIONS IS 60.IF MEAN OF FIRST 13 OBSERVATIONS IS 70 AND MEAN OF LAST 13 OBSERVATION IS 50.FIND MIDDLE OBSERVATIONS WHEN ARRANGED IN ASCENDING ORDER.I WANT THE THE ANSWER FR THIS QUE

Answer 1

SOLUTION

GIVEN

• Mean of 25 observations is 60.

• Mean of first 13 observations is 70

• Mean of last 13 Observation is 50

TO DETERMINE

The middle Observation when arranged in Ascending Order

EVALUATION

Let sum of first 12 observations = x , Middle term = y, sum of last 12 observations = z

Here it is given that Mean of first 13 observations is 70

∴ Sum of of first 13 observations = 13 × 70 = 910

∴ x + y = 910 - - - - Equation 1

Again Mean of last 13 Observation is 50

∴ Sum of of last 13 observations = 13 × 50 = 650

∴ y + z = 650 - - - - Equation 2

Again Mean of 25 observations is 60

∴ Sum of 25 observations = 25 × 60 = 1500

∴ x + y + z = 1500 - - - - - Equation 3

Equation (1) + (2) - (3) gives

( x + 2y + z ) - ( x + y + z ) = 910 + 650 - 1500

$\implies \sf{y = 60}$

FINAL ANSWER

Hence the middle Observation = 60

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Answer 2

Given :-

• Mean of 25 observations = 60 .
• Mean of first 13 observations = 70 .
• Mean of Last 13 observations = 50 .

To Find :-

• Middle observations when arranged in ascending order ?

Solution :-

we know that,

• Mean = (Sum of observations / Total No. of observations.)

So,

→ Mean of 25 observations = 60 .

→ 60 = (sum of observations / 25)

→ sum of all observations = 60 * 25 = 1500 ------- Eqn.(1)

Similarly,

→ Mean of first 13 observations = 70 .

→ 70 = (sum of observations / 13)

→ sum of first 13 observations = 70 * 13 = 910 ------- Eqn.(2)

again,

→ Mean of Last 13 observations = 50 .

→ 50 = (sum of observations / 13)

→ sum of last 13 observations = 50 * 13 = 650 ------- Eqn.(3)

therefore,

→ Middle observation = (sum of first 13 observations + sum of last 13 observations) - sum of all observations

→ Middle observation = [Eqn.(2) + Eqn.(3)] - Eqn.(1)

→ Middle observation = (910 + 650) - 1500

→ Middle observation = 1560 - 1500

→ Middle observation = 60 . (Ans.)

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