Multiple choice

In the frequency distribution of discrete data given below the frequency $x$ against value $0$ is missing Variable $x$ $0$ $1$ $2$ $3$ $4$ $5$ Frequency $f$ $x$ $20$ $40$ $40$ $20$ $4$ If the mean is $2.5$ then the missing frequency $x$ will be __________

  1. $0$
  2. $1$
  3. $3$
  4. $4$
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D Correct answer
Explanation

The mean is calculated as (sum of (variable * frequency)) / (sum of frequencies). Sum of frequencies = x + 20 + 40 + 40 + 20 + 4 = x + 124. Sum of (variable * frequency) = (0*x) + (1*20) + (2*40) + (3*40) + (4*20) + (5*4) = 0 + 20 + 80 + 120 + 80 + 20 = 320. So, 320 / (x + 124) = 2.5. Solving for x: 320 = 2.5x + 310, so 2.5x = 10, x = 4.

AI explanation

The formula for the mean of a discrete frequency distribution is the sum of the products of values and frequencies divided by the total frequency. The sum of the products is (0*x) + (1*20) + (2*40) + (3*40) + (4*20) + (5*4), which equals 0 + 20 + 80 + 120 + 80 + 20 = 320. The total frequency is x + 20 + 40 + 40 + 20 + 4 = x + 124. Setting the mean to 2.5 gives 320 / (x + 124) = 2.5, which simplifies to 2.5x + 310 = 320, so x = 4.

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