Multiple choice

If the mean of the following frequency distribution is $5$, then $b$ is equal to $x_i$: 3 5 7 4 $f_i$: 2 $a$ 5 $b$

  1. $10$
  2. $6$
  3. $8$
  4. None of these

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Interpreting the table as xi = 3, 5, 7, 4 and fi = 2, a, 5, b, the mean equation is (41 + 5a + 4b)/(7 + a + b) = 5. Simplifying gives b = 6.

AI explanation

Using the arithmetic mean formula for frequency distributions, we get (6 + 5a + 35 + 4b) / (2 + a + 5 + b) = 5, where the total frequency equals 7 + a + b. This simplifies to 41 + 5a + 4b = 35 + 5a + 5b, meaning 41 = 35 + b and therefore b = 6.