Multiple choice

If the mean of the following distribution is $10$, find the value of $m$. $X$ $12$ $4$ $6 + m$ $8$ $10$ $F$ $10$ $15$ $25$ $24$ $16$

  1. $7.72$
  2. $8.72$
  3. $6.72$
  4. $9.72$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mean = Sum(f*x) / Sum(f). Sum(f) = 10+15+25+24+16 = 90. Sum(f*x) = 12*10 + 4*15 + (6+m)*25 + 8*24 + 10*16 = 120 + 60 + 150 + 25m + 192 + 160 = 682 + 25m. Mean = (682 + 25m) / 90 = 10. 682 + 25m = 900. 25m = 218. m = 8.72.

AI explanation

Using the mean formula, the total sum of observations is (12*10) + (4*15) + ((6+m)*25) + (8*24) + (10*16), which equals 120 + 60 + 150 + 25m + 192 + 160 = 682 + 25m. The total frequency is 10 + 15 + 25 + 24 + 16 = 90. Since the mean is 10, the total sum must be 90 * 10 = 900. Setting up the equation 682 + 25m = 900 gives 25m = 218, so m equals 8.72.

Keep practicing — related questions