Read the information given below carefully and answer the question that follows:

(A) If the mean of 5 numbers is 15 and then if 27 is included to the numbers, then the mean of the 6 numbers shall be 17

(B) The mean of marks of 300 students is 60, the mean of the top 100 students' marks is 80 and the mean of the last 100 students is 50, then the mean of the marks of the rest of the 100 students of the group is 60.

(C) The mean and median of 5 observations is 9 and 8 respectively, if 1 is subtracted from each observation, then the new mean and median shall be 8 and 7 respectively

Choose the correct answer from the options given below:

Statement (A):

Mean of 5 numbers = 15

Sum of 5 numbers = 15 × 5 = 75

When 27 is added:

New sum = 75 + 27 = 102

New mean = $\dfrac{102}{6}$

$= 17$

Statement (A) is TRUE.

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Statement (B):

Total students = 300, Mean = 60

Total marks = 60 × 300 = 18,000

Top 100 students have mean = 80

Marks of top 100 = 80 × 100 = 8,000

Last 100 students have mean = 50

Marks of last 100 = 50 × 100 = 5,000

Marks of middle 100 students:

$= 18,000 - 8,000 - 5,000$

$= 5,000$

Mean of middle 100 students:

$= \dfrac{5,000}{100}$

$= 50$

The claim states the mean is 60, but the actual mean is 50.

Statement (B) is FALSE.

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Statement (C):

Original mean = 9, Median = 8

Sum of 5 observations = 9 × 5 = 45

When 1 is subtracted from each observation, total reduction = 5 × 1 = 5

New sum = 45 - 5 = 40

New mean:

$= \dfrac{40}{5}$

$= 8$

When 1 is subtracted from all observations, every value shifts down by 1.

New median = 8 - 1 = 7

Statement (C) is TRUE.

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Statements (A) and (C) are correct, while Statement (B) is incorrect.