Multiple choice

If $6, 4, 8$ and $3$ occur with frequencies $4, 2, 5$ and $1$ respectively, then the arithmetic mean is __________.

  1. $6.25$
  2. $6.75$
  3. $6.5$
  4. $6$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mean = (Sum of (value * frequency)) / (Sum of frequencies). Calculation: (6*4 + 4*2 + 8*5 + 3*1) / (4+2+5+1) = (24 + 8 + 40 + 3) / 12 = 75 / 12 = 6.25.

AI explanation

The direct method for calculating the arithmetic mean for ungrouped frequency data is the sum of the observations multiplied by their respective frequencies, divided by the total frequency. Here, the sum of the products is 6 multiplied by 4 plus 4 multiplied by 2 plus 8 multiplied by 5 plus 3 multiplied by 1, which equals 24 plus 8 plus 40 plus 3, totaling 75. Dividing this sum by the total number of observations (4 plus 2 plus 5 plus 1 equals 12) gives an arithmetic mean of 75 divided by 12, which is 6.25.

Keep practicing — related questions