Multiple choice

If the arithmetic mean of the following distribution is $8.2$, then $a$ is equal to $x_i$: 1 3 5 9 11 13 $f_i$: 3 2 7 a 4 8

  1. $5$
  2. $6$
  3. $9$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mean = sum(f*x) / sum(f). Sum(f*x) = 1*3 + 3*2 + 5*7 + 9*a + 11*4 + 13*8 = 3 + 6 + 35 + 9a + 44 + 104 = 192 + 9a. Sum(f) = 3+2+7+a+4+8 = 24+a. (192+9a)/(24+a) = 8.2. 192+9a = 196.8 + 8.2a. 0.8a = 4.8. a = 6.

AI explanation

The arithmetic mean formula is the sum of the products of values and their frequencies divided by the total frequency. The sum of the products is (1 times 3) plus (3 times 2) plus (5 times 7) plus (9 times a) plus (11 times 4) plus (13 times 8), which equals 190 plus 9a. The total frequency is 24 plus a. Setting the mean to 8.2 gives 190 plus 9a equals 8.2 multiplied by (24 plus a), which simplifies to 190 plus 9a equals 196.8 plus 8.2a. Solving for a gives 0.8a equals 6.8, meaning a is 6.

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