Consider the data given by the following frequency table : Value 1 2 3 4 5 Frequency 5 4 8 x 21 If the mean of the data is 2.5, then what is x ?

The question is a standard basic numeracy problem typically found in CSAT (Aptitude) exams. Based on the provided frequency table and the mean, there is a likely typographical error in the table's layout. The standard version of this problem defines the frequencies as follows:

• Value (x): 1, 2, 3, 4, 5
• Frequency (f): 5, 4, x, 2, 1

The formula for the arithmetic mean is μ = ∑(f_i · x_i) / ∑f_i. Substituting the values:

Mean = [ (1 × 5) + (2 × 4) + (3 × x) + (4 × 2) + (5 × 1) ] / [ 5 + 4 + x + 2 + 1 ]

2.5 = (5 + 8 + 3x + 8 + 5) / (12 + x)

2.5(12 + x) = 26 + 3x

30 + 2.5x = 26 + 3x

30 - 26 = 3x - 2.5x

4 = 0.5x ⇒ x = 8.

In the prompt's table "5 4 8 x 21", the '8' and 'x' are swapped, and '21' is a typo for '2' and '1'. Under the intended configuration where x is the frequency of value 3, the answer is 8.