Q)  The mean of the following frequency distribution is 35. Find the values of x and y, if the sum of frequencies is 25:

(Q35 – 30/1/1 – CBSE 2026 Question Paper)

Ans:

Step 1: Le’ts calculate the sum of frequencies:

By 1st condition, we are given that sum of frequencies is 25

From table, we have sum of frequencies as (17 + x + y)

∴ 25 = 17 + x + y

∴ x + y = 25 – 17

∴ x + y = 8 …………. (i)

Step 2: Next, we calculate mid values x, fx and ∑fx for each class:

Next, we apply mean formula:

∴ Mean =

∴ Mean =

Step 3: By 1st condition, we are given that mean value is 35

∴ 35 =

∴ 35 (17 + x + y) = (345 + 10 x + 25 y)

∴ 595 + 35 x + 35 y = 345 + 10 x + 25 y

∴ 595 + 35 x + 35 y – (345 + 10 x + 25 y) = 0

∴ 250 + 25 x + 10 y = 0

∴ 5 x + 2 y + 50 = 0 …… (ii)

Step 4: Let’s solve equations (i) and (ii) for values of x and y:

Let’s multiply equation (i) by 2 and subtract from equation (ii):

∴ (5 x + 2 y + 50) – 2 (x + y) = 0 – 2(8)

∴ 5 x + 2 y + 50 – 2 x – 2 y = – 16

∴ 5 x + 2 y – 2 x – 2 y = – 16 – 50 = – 66

∴ 3 x = – 66

∴ x =

∴ x = – 22

Step 5: Let’s put value of x in equation (i), we get:

∵ x + y = 8

∴ (- 22) + y = 8

∴ y – 22 = 8

∴ y = 8 + 22

∴ y = 30

Therefore, the values of x and y are – 22 and 30 respectively.

Check: Let’s check if x = – 22 and y = 30 is correct or not.
Value of ∑ f = 17 + x + y = 17 – 22 + 30 = 25. It satisfies given condition.
Now ∑ f x = 345 + 10 x + 25 y = 345 + (10 x -22) + (25 x 30) = 345 – 220 + 750 = 875 and we have ∑ f = 25
∴ Mean value = = = 35. It satisfies given 2nd condition also.
Since both given conditions are satisfied, Hence, our answer is correct.

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