Multiple choice

Find the value of $x$, if the mean of the following distribution is $7.5$ x: 3 5 7 9 11 13 f: 6 8 15 x 8 4

  1. $3$
  2. $2$
  3. $1$
  4. $7$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using mean = sum of xf divided by sum of f, we get (303 + 9x)/(41 + x) = 7.5. Solving gives 303 + 9x = 307.5 + 7.5x, so x = 3.

AI explanation

Using the direct method for the arithmetic mean, we calculate the sum of products of observations and frequencies as (3 times 6) plus (5 times 8) plus (7 times 15) plus (9x) plus (11 times 8) plus (13 times 4), which equals 297 plus 9x. The total frequency is 6 plus 8 plus 15 plus x plus 8 plus 4, which equals 41 plus x. Setting the mean equal to 7.5 gives the equation (297 plus 9x) divided by (41 plus x) equals 7.5. Solving this yields 297 plus 9x equals 307.5 plus 7.5x, so 1.5x equals 10.5, and x equals 3.

Keep practicing — related questions